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Sharma K, Bhat VK, Liu J. Second leap hyper-Zagreb coindex of certain benzenoid structures and their polymomials. COMPUT THEOR CHEM 2023. [DOI: 10.1016/j.comptc.2023.114088] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/08/2023]
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2
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Zaman S, Jalani M, Ullah A, Ali M, Shahzadi T. On the topological descriptors and structural analysis of cerium oxide nanostructures. Chem Pap 2023. [DOI: 10.1007/s11696-023-02675-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
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3
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Raza Z, Akhter S, Shang Y. Expected value of first Zagreb connection index in random cyclooctatetraene chain, random polyphenyls chain, and random chain network. Front Chem 2023; 10:1067874. [PMID: 36688029 PMCID: PMC9846538 DOI: 10.3389/fchem.2022.1067874] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2022] [Accepted: 12/07/2022] [Indexed: 01/05/2023] Open
Abstract
The Zagreb connection indices are the known topological descriptors of the graphs that are constructed from the connection cardinality (degree of given nodes lying at a distance 2) presented in 1972 to determine the total electron energy of the alternate hydrocarbons. For a long time, these connection indices did not receive much research attention. Ali and Trinajstić [Mol. Inform. 37, Art. No. 1800008, 2018] examined the Zagreb connection indices and found that they compared to basic Zagreb indices and that they provide a finer value for the correlation coefficient for the 13 physico-chemical characteristics of the octane isomers. This article acquires the formulae of expected values of the first Zagreb connection index of a random cyclooctatetraene chain, a random polyphenyls chain, and a random chain network with l number of octagons, hexagons, and pentagons, respectively. The article presents extreme and average values of all the above random chains concerning a set of special chains, including the meta-chain, the ortho-chain, and the para-chain.
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Affiliation(s)
- Zahid Raza
- Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, United Arab Emirates,*Correspondence: Zahid Raza, ; Yilun Shang,
| | - Shehnaz Akhter
- School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan
| | - Yilun Shang
- Department of Computer and Information Sciences, Northumbria University, Newcastle upon Tyne, United Kingdom,*Correspondence: Zahid Raza, ; Yilun Shang,
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Banerjee S, Ash T, Debnath T, Das AK. Dual modification to stabilize Non-IPR C 72 fullerene: A new theoretical strategy. J Mol Graph Model 2022; 117:108289. [PMID: 35964364 DOI: 10.1016/j.jmgm.2022.108289] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2022] [Revised: 07/21/2022] [Accepted: 08/01/2022] [Indexed: 01/14/2023]
Abstract
The stabilization of non-IPR fullerenes for their isolation and characterization is an area of recent interest. In the present study, we have explored the stabilization techniques of C72 isomers via endo and exo-modifications and finally approached dual modification. A total of four isomers of C72 have been considered in this study; among them, one is IPR derivative (1), and the rest are non-IPR derivatives with one (2) and two (3 and 4) fused pentagon rings. First, we have studied the endohedral modification by encapsulating one and two La atoms in the C72 cavity. Secondly, we have exohedrally modified the C72 isomers via chlorination by adding four and eight chlorides, respectively. Our final approach is to study the dual modification, where we have implemented both endo exo-modifications together. This dual modification can be achieved in two ways: exo followed by endo and endo followed by exo. For each modification, the relative stability of every modified C72 derivative has been checked by calculating the relative energy with respect to the most stable modified analogue. To find out whether these modifications are energetically feasible or not, we have calculated the binding energy of each modified C72 isomer. The binding energy calculation reveals that the encapsulation and exo-modification techniques are good enough to stabilize the non-IPR C72 derivatives. Moreover, the effectiveness of dual modification has also been established from the enhanced binding energy compared to either endo- or exo-modification. We have also studied the NPA charges on the encapsulated La atoms for each endo- and dual-modified C72 derivative. Furthermore, the AIM study has also been perceived to find out the interaction between the La atom and the fullerene cages for both mono- and di-encapsulated fullerene derivatives and also between La-La centres for di-encapsulated derivatives. Overall, the present theoretical study will provide an idea about the stability of the modified C72 derivatives, which will help the experimentalists to design new strategies for synthesizing modified non-IPR fullerene derivatives that have vast applications in the medicinal and industrial fields.
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Affiliation(s)
- Soumadip Banerjee
- School of Mathematical & Computational Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, 700032, India
| | - Tamalika Ash
- School of Mathematical & Computational Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, 700032, India
| | - Tanay Debnath
- School of Mathematical & Computational Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, 700032, India.
| | - Abhijit K Das
- School of Mathematical & Computational Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, 700032, India.
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Shooshtari H, Sheikholeslami SM, Amjadi J. The Expected Values of Hyper Zagreb and Forgotten Topological Indices in Random Phenylene Chains. Polycycl Aromat Compd 2022. [DOI: 10.1080/10406638.2022.2131851] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Hajar Shooshtari
- Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
| | | | - Jafar Amjadi
- Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
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Affiliation(s)
- Maria Singaraj Rosary
- Department of Mathematics, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Chennai, India
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Zhu W, Geng X. Enumeration of the Multiplicative Degree-Kirchhoff Index in the Random Polygonal Chains. Molecules 2022; 27:5669. [PMID: 36080441 DOI: 10.3390/molecules27175669] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/11/2022] [Revised: 08/21/2022] [Accepted: 08/29/2022] [Indexed: 11/24/2022]
Abstract
Multiplicative degree-Kirchhoff index is a very interesting topological index. In this article, we compute analytical expression for the expected value of the Multiplicative degree-Kirchhoff index in a random polygonal. Based on the result above, we also get the Multiplicative degree-Kirchhoff index of all polygonal chains with extremal values and average values.
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Imran M, Siddiqui MK, Javed S, Sherin L, Khalid S, Asghar W. On Analysis of Heat of Formation and Entropy Measures for Indium Phosphide. ARAB J CHEM 2022. [DOI: 10.1016/j.arabjc.2022.104218] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
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Yin J, Tian Y. Super Connected Direct Product of Graphs and Cycles. Axioms 2022; 11:277. [DOI: 10.3390/axioms11060277] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
The topology of an interconnection network can be modeled by a graph G=(V(G),E(G)). The connectivity of graph G is a parameter used to measure the reliability of a corresponding network. The direct product is an important graph product. This paper mainly focuses on the super connectedness of the direct product of graphs and cycles. The connectivity of G, denoted by κ(G), is the size of a minimum vertex set S⊆V(G) such that G−S is not connected or has only one vertex. The graph G is said to be super connected, simply super-κ, if every minimum vertex cut is the neighborhood of a vertex with minimum degree. The direct product of two graphs G and H, denoted by G×H, is the graph with vertex set V(G×H)=V(G)×V(H) and edge set E(G×H)={(u1,v1)(u2,v2)|u1u2∈E(G),v1v2∈E(H)}. In this paper, we give some sufficient conditions for the direct product G×Cn to be super connected, where Cn is the cycle on n vertices. Furthermore, those sufficient conditions are the best possible.
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Abstract
A double Roman dominating function on a graph G=(V,E) is a function f:V→{0,1,2,3}, satisfying the condition that every vertex u for which f(u)=1 is adjacent to at least one vertex assigned 2 or 3, and every vertex u with f(u)=0 is adjacent to at least one vertex assigned 3 or at least two vertices assigned 2. The weight of f equals the sum w(f)=∑v∈Vf(v). The minimum weight of a double Roman dominating function of G is called the double Roman domination number γdR(G) of a graph G. We obtain tight bounds and in some cases closed expressions for the double Roman domination number of generalized Petersen graphs P(ck,k). In short, we prove that γdR(P(ck,k))=32ck+ε, where limc→∞,k→∞εck=0.
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Hayat S, Khan A, Zhong Y. On Resolvability- and Domination-Related Parameters of Complete Multipartite Graphs. Mathematics 2022; 10:1815. [DOI: 10.3390/math10111815] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Graphs of order n with fault-tolerant metric dimension n have recently been characterized.This paper points out an error in the proof of this characterization. We show that the complete multipartite graphs also have the fault-tolerant metric dimension n, which provides an infinite family of counterexamples to the characterization. Furthermore, we find exact values of the metric, edge metric, mixed-metric dimensions, the domination number, locating-dominating number, and metric-locating-dominating number for the complete multipartite graphs. These results generalize various results in the literature from complete bipartite to complete multipartite graphs.
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Planat M, Amaral MM, Fang F, Chester D, Aschheim R, Irwin K. Character Varieties and Algebraic Surfaces for the Topology of Quantum Computing. Symmetry (Basel) 2022; 14:915. [DOI: 10.3390/sym14050915] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
It is shown that the representation theory of some finitely presented groups thanks to their SL2(C) character variety is related to algebraic surfaces. We make use of the Enriques–Kodaira classification of algebraic surfaces and related topological tools to make such surfaces explicit. We study the connection of SL2(C) character varieties to topological quantum computing (TQC) as an alternative to the concept of anyons. The Hopf link H, whose character variety is a Del Pezzo surface fH (the trace of the commutator), is the kernel of our view of TQC. Qutrit and two-qubit magic state computing, derived from the trefoil knot in our previous work, may be seen as TQC from the Hopf link. The character variety of some two-generator Bianchi groups, as well as that of the fundamental group for the singular fibers E˜6 and D˜4 contain fH. A surface birationally equivalent to a K3 surface is another compound of their character varieties.
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Iqbal MA, Imran M, Siddiqui MK, Zaighum MA. Computing Molecular Topological Descriptors of Polymeric Networks Modeled by Sierpinski Networks. Polycycl Aromat Compd 2022. [DOI: 10.1080/10406638.2020.1783331] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Muhamamd Azhar Iqbal
- Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan
| | - Muhammad Imran
- Department of Mathematical Sciences, United Arab Emirates University, Al Ain, United Arab Emirates
| | | | - Muhammad Asad Zaighum
- Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan
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Khabyah AA, Zaman S, Koam ANA, Ahmad A, Ullah A. Minimum Zagreb Eccentricity Indices of Two-Mode Network with Applications in Boiling Point and Benzenoid Hydrocarbons. Mathematics 2022; 10:1393. [DOI: 10.3390/math10091393] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
A two-mode network is a type of network in which nodes can be divided into two sets in such a way that links can be established between different types of nodes. The relationship between two separate sets of entities can be modeled as a bipartite network. In computer networks data is transmitted in form of packets between source to destination. Such packet-switched networks rely on routing protocols to select the best path. Configurations of these protocols depends on the network acquirements; that is why one routing protocol might be efficient for one network and may be inefficient for a other. Because some protocols deal with hop-count (number of nodes in the path) while others deal with distance vector. This paper investigates the minimum transmission in two-mode networks. Based on some parameters, we obtained the minimum transmission between the class of all connected n-nodes in bipartite networks. These parameters are helpful to modify or change the path of a given network. Furthermore, by using least squares fit, we discussed some numerical results of the regression model of the boiling point in benzenoid hydrocarbons. The results show that the correlation of the boiling point in benzenoid hydrocarbons of the first Zagreb eccentricity index gives better result as compare to the correlation of second Zagreb eccentricity index. In case of a connected network, the first Zagreb eccentricity index ξ1(ℵ) is defined as the sum of the square of eccentricities of the nodes, and the second Zagreb eccentricity index ξ2(ℵ) is defined as the sum of the product of eccentricities of the adjacent nodes. This article deals with the minimum transmission with respect to ξi(ℵ), for i=1,2 among all n-node extremal bipartite networks with given matching number, diameter, node connectivity and link connectivity.
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Maungchang R, Detphumi C, Khachorncharoenkul P, Suksumran T. Hamiltonian Cycles in Cayley Graphs of Gyrogroups. Mathematics 2022; 10:1251. [DOI: 10.3390/math10081251] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
In this study, we investigate Hamiltonian cycles in the right-Cayley graphs of gyrogroups. More specifically, we give a gyrogroup version of the factor group lemma and show that some right-Cayley graphs of certain gyrogroups are Hamiltonian.
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17
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Lu H, Zhu Z. The Extremal Structures of r-Uniform Unicyclic Hypergraphs on the Signless Laplacian Estrada Index. Mathematics 2022; 10:941. [DOI: 10.3390/math10060941] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
SLEE has various applications in a large variety of problems. The signless Laplacian Estrada index of a hypergraph H is defined as SLEE(H)=∑i=1neλi(Q), where λ1(Q),λ2(Q),…,λn(Q) are the eigenvalues of the signless Laplacian matrix of H. In this paper, we characterize the unique r-uniform unicyclic hypergraphs with maximum and minimum SLEE.
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Kirmani SAK, Ali P, Ahmad J, Tang Z. Topological Coindices and Quantitative Structure-Property Analysis of Antiviral Drugs Investigated in the Treatment of COVID-19. J CHEM-NY 2022; 2022:1-15. [DOI: 10.1155/2022/3036655] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
SARS-CoV-2 is a new strain of coronavirus family that has never been previously detected in humans. This has grown into a huge public health issue that has affected people all around the world. Presently, there is no specific antiviral treatment for COVID-19. To tackle the outbreak, a number of drugs are being explored or have been utilized based on past experience. A molecular descriptor (or topological index) is a numerical value that describes a compound’s molecular structure and has been successfully employed in many QSPR/QSAR investigations to represent several physicochemical attributes. In order to determine topological characteristics of graphs, coindices (topological) take nonadjacent pair of vertices into account. In this study, we introduced CoM-polynomial and numerous degree-based topological coindices for several antiviral medicines such as lopinavir, ritonavir remdesivir, hydroxychloroquine, chloroquine, theaflavin, thalidomide, and arbidol which were studied using the CoM-polynomial approach. In the QSPR model, the linear regression approach is used to analyze the relationships between physicochemical properties and topological coindices. The findings show that the topological coindices under investigation have a substantial relationship with the physicochemical properties of possible antiviral medicines in question. As a result, topological coindices may be effective tools for studying antiviral drugs in the future for QSPR analyses.
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Yang F, Sun Q, Zhou H, Zhang C. Cayley Graphs Defined by Systems of Equations. Axioms 2022; 11:100. [DOI: 10.3390/axioms11030100] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Let R be a finite ring. In this paper, we mainly explore the conditions to ensure the graph BΓn defined by a system of equations {fi|i=2,…,n} to be a Cayley graph or a Hamiltonian graph. More precisely, we prove that BΓn is a Cayley graph with G=⟨ϕ,A⟩ a group of dihedral type if and only if the system Fn={fi|i=2,…,n} is Cayley graphic of dihedral type in R. As an application, the well-known Lova´sz Conjecture, which states that any finite connected Cayley graph has a Hamilton cycle, holds for the connected BΓn defined by Cayley graphic system Fn of dihedral type in the field GF(pk).
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Mrissa M, Tošić A, Hrovatin N, Aslam S, Dávid B, Hajdu L, Krész M, Brodnik A, Kavšek B. Privacy-Aware and Secure Decentralized Air Quality Monitoring. Applied Sciences 2022; 12:2147. [DOI: 10.3390/app12042147] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Indoor Air Quality monitoring is a major asset to improving quality of life and building management. Today, the evolution of embedded technologies allows the implementation of such monitoring on the edge of the network. However, several concerns need to be addressed related to data security and privacy, routing and sink placement optimization, protection from external monitoring, and distributed data mining. In this paper, we describe an integrated framework that features distributed storage, blockchain-based Role-based Access Control, onion routing, routing and sink placement optimization, and distributed data mining to answer these concerns. We describe the organization of our contribution and show its relevance with simulations and experiments over a set of use cases.
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Qi J, Fang M, Geng X. The Expected Value for the Wiener Index in the Random Spiro Chains. Polycycl Aromat Compd 2022. [DOI: 10.1080/10406638.2022.2038218] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Jinfeng Qi
- School of Mathematics and Big Data, Anhui University of Science & Technology, Huainan, China
| | - Minglei Fang
- School of Mathematics and Big Data, Anhui University of Science & Technology, Huainan, China
| | - Xianya Geng
- School of Mathematics and Big Data, Anhui University of Science & Technology, Huainan, China
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22
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Sun Y, Li H, Cao Y. Effects of COVID-Induced Public Anxiety on European Stock Markets: Evidence From a Fear-Based Algorithmic Trading System. Front Psychol 2022; 12:780992. [PMID: 35095663 PMCID: PMC8795696 DOI: 10.3389/fpsyg.2021.780992] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2021] [Accepted: 12/06/2021] [Indexed: 12/03/2022] Open
Abstract
The effect of COVID-induced public anxiety on stock markets, particularly in European stock market returns, is examined in this research. The search volumes for the notion of COVID-19 gathered by Google Trends and Wikipedia were used as proxies for COVID-induced public anxiety. COVID-induced public anxiety was shown to be linked with negative returns in European stock markets when a panel data method was used to a sample of data from 14 European stock markets from January 2, 2020 to September 17, 2020. Using an automated trading system, we used this finding to suggest investment methods based on COVID-induced anxiety. The findings of back-testing indicate that these techniques have the potential to generate exceptional profits. These results have significant consequences for government officials, the media, and investors.
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Affiliation(s)
- Yunpeng Sun
- School of Economics, Tianjin University of Commerce, Tianjin, China
| | - Haoning Li
- School of Economics, Tianjin University of Commerce, Tianjin, China
| | - Yuning Cao
- School of Economics, Tianjin University of Commerce, Tianjin, China
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Ghorbaninejad M, Ghobadi S. The F-index and F-coindex of four operations on Trees. Journal of Information and Optimization Sciences 2022. [DOI: 10.1080/02522667.2021.1964728] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Mobina Ghorbaninejad
- Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
| | - Sirous Ghobadi
- Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
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Rosary MS. On Reverse Valency Based Topological Indices of Metal–Organic Framework. Polycycl Aromat Compd 2022. [DOI: 10.1080/10406638.2021.2021255] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Maria Singaraj Rosary
- Department of Mathematics, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Chennai, India
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Abstract
A double Roman dominating function on a graph G=(V,E) is a function f:V→{0,1,2,3} satisfying the condition that every vertex u for which f(u)=0 is adjacent to at least one vertex assigned 3 or at least two vertices assigned 2, and every vertex u with f(u)=1 is adjacent to at least one vertex assigned 2 or 3. The weight of f equals w(f)=∑v∈Vf(v). The double Roman domination number γdR(G) of a graph G equals the minimum weight of a double Roman dominating function of G. We obtain closed expressions for the double Roman domination number of generalized Petersen graphs P(5k,k). It is proven that γdR(P(5k,k))=8k for k≡2,3mod5 and 8k≤γdR(P(5k,k))≤8k+2 for k≡0,1,4mod5. We also improve the upper bounds for generalized Petersen graphs P(20k,k).
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Abstract
The modified second Zagreb index, symmetric difference index, inverse symmetric index, and augmented Zagreb index are among the molecular descriptors which have good correlations with some physicochemical properties (such as formation heat, total surface area, etc.) of chemical compounds. By a random cyclooctane chain, we mean a molecular graph of a saturated hydrocarbon containing at least two rings such that all rings are cyclooctane, every ring is joint with at most two other rings through a single bond, and exactly two rings are joint with one other ring. In this article, our main purpose is to determine the expected values of the aforementioned molecular descriptors of random cyclooctane chains explicitly. We also make comparisons in the form of explicit formulae and numerical tables consisting of the expected values of the considered descriptors of random cyclooctane chains. Moreover, we outline the graphical profiles of these comparisons among the mentioned descriptors.
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Ayache A, Alameri A, Alsharafi M, Ahmed H. The Second Hyper-Zagreb Coindex of Chemical Graphs and Some Applications. J CHEM-NY 2021; 2021:1-8. [DOI: 10.1155/2021/3687533] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The second hyper-Zagreb coindex is an efficient topological index that enables us to describe a molecule from its molecular graph. In this current study, we shall evaluate the second hyper-Zagreb coindex of some chemical graphs. In this study, we compute the value of the second hyper-Zagreb coindex of some chemical graph structures such as sildenafil, aspirin, and nicotine. We also present explicit formulas of the second hyper-Zagreb coindex of any graph that results from some interesting graphical operations such as tensor product, Cartesian product, composition, and strong product, and apply them on a q-multiwalled nanotorus.
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Ezadi M. A further study on edge-distance-balanced property of the generalized Petersen graphs GP(6 n+8, 3). Journal of Information and Optimization Sciences 2021. [DOI: 10.1080/02522667.2021.1939959] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Mahboubeh Ezadi
- Department of Mathematics, Chalous Branch, Islamic Azad University, Chalous, Iran
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Abstract
Given a connected graph G=(V(G),E(G)), a set S⊆V(G) is said to be a k-metric generator for G if any pair of different vertices in V(G) is distinguished by at least k elements of S. A metric generator of minimum cardinality among all k-metric generators is called a k-metric basis and its cardinality is the k-metric dimension of G. We initially present a linear programming problem that describes the problem of finding the k-metric dimension and a k-metric basis of a graph G. Then we conducted a study on the k-metric dimension of a unicyclic graph.
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Yang J, Muhammad MH, Siddiqui MK, Hanif MF, Nasir M, Ali S, Liu JB. Topological Co-indices of Hydroxyethyl Starch Conjugated with Hydroxychloroquine Used for COVID-19 Treatment. Polycycl Aromat Compd 2021. [DOI: 10.1080/10406638.2021.1996407] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Affiliation(s)
- Jun Yang
- GongQing Institute of Science and Technology, Gong Qing, China
| | - Mehwish Hussain Muhammad
- College of Chemistry, School of Chemical Engineering and Energy, Zhengzhou University, Zhengzhou, China
| | | | | | - Muhammad Nasir
- Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
| | - Safdar Ali
- Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
| | - Jia-Bao Liu
- School of Mathematics and Physics, Anhui Jianzhu University, Hefei, China
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31
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Yang H, Naeem M, Jamil MK. Topological Descriptors of M-Carbon . J CHEM-NY 2021; 2021:1-14. [DOI: 10.1155/2021/8792585] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We have studied topological indices of the one the hardest crystal structures in a given chemical system, namely, M-carbon. These structures are based and obtained by the famous algorithm USPEX. The computations and applications of topological indices in the study of chemical structures is growing exponentially. Our aim in this article is to compare and compute some well-known topological indices based on degree and sum of degrees, namely, general Randić indices, Zagreb indices, atom bond connectivity index, geometric arithmetic index, new Zagreb indices, fourth atom bond connectivity index, fifth geometric arithmetic index, and Sanskruti index of the M-carbon
. Moreover, we have also computed closed formulas for these indices.
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32
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Affiliation(s)
- Abdul Rauf
- Department of Mathematics, Air University Multan Campus, Multan, Pakistan
| | - Muhammad Naeem
- Department of Mathematics, Air University Multan Campus, Multan, Pakistan
| | - Saba Maqbool
- Department of Mathematics, Air University Multan Campus, Multan, Pakistan
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33
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Zhang D, Li C, Chao F. On the Total Neighbor Sum Distinguishing Index of IC-Planar Graphs. Symmetry (Basel) 2021; 13:1787. [DOI: 10.3390/sym13101787] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
A proper total k-coloring ϕ of G with ∑z∈EG(u)∪{u}ϕ(z)≠∑z∈EG(v)∪{v}ϕ(z) for each uv∈E(G) is called a total neighbor sum distinguishing k-coloring, where EG(u)={uv|uv∈E(G)}. Pilśniak and Woźniak conjectured that every graph with maximum degree Δ exists a total neighbor sum distinguishing (Δ+3)-coloring. In this paper, we proved that any IC-planar graph with Δ≥12 satisfies this conjecture, which improves the result of Song and Xu.
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34
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Slepičková Kasálková N, Slepička P, Švorčík V. Carbon Nanostructures, Nanolayers, and Their Composites. Nanomaterials (Basel) 2021; 11:2368. [PMID: 34578684 DOI: 10.3390/nano11092368] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/27/2021] [Accepted: 09/08/2021] [Indexed: 01/15/2023]
Abstract
The versatility of the arrangement of C atoms with the formation of different allotropes and phases has led to the discovery of several new structures with unique properties. Carbon nanomaterials are currently very attractive nanomaterials due to their unique physical, chemical, and biological properties. One of these is the development of superconductivity, for example, in graphite intercalated superconductors, single-walled carbon nanotubes, B-doped diamond, etc. Not only various forms of carbon materials but also carbon-related materials have aroused extraordinary theoretical and experimental interest. Hybrid carbon materials are good candidates for high current densities at low applied electric fields due to their negative electron affinity. The right combination of two different nanostructures, CNF or carbon nanotubes and nanoparticles, has led to some very interesting sensors with applications in electrochemical biosensors, biomolecules, and pharmaceutical compounds. Carbon materials have a number of unique properties. In order to increase their potential application and applicability in different industries and under different conditions, they are often combined with other types of material (most often polymers or metals). The resulting composite materials have significantly improved properties.
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35
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Rafiullah M, Siddiqui HMA, Siddiqui MK, Dhlamini M, Haq Bokhary SA. On Degree-Based Topological Indices for Strong Double Graphs. J CHEM-NY 2021; 2021:1-12. [DOI: 10.1155/2021/4852459] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
A topological index is a characteristic value which represents some structural properties of a chemical graph. We study strong double graphs and their generalization to compute Zagreb indices and Zagreb coindices. We provide their explicit computing formulas along with an algorithm to generate and verify the results. We also find the relation between these indices. A 3D graphical representation and graphs are also presented to understand the dynamics of the aforementioned topological indices.
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36
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Affiliation(s)
- Rongbing Huang
- School of Computer Science, Chengdu University, Chengdu, China
| | - Mehwish Hussain Muhammad
- College of chemistry, School of Chemical Engineering and Energy, Zhengzhou University, Zhengzhou, China
| | | | - Muhammad Nasir
- Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
| | - Murat Cancan
- Faculty of Education, Van Yuzuncu Yil University, Van, Turkey
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37
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Almerich-chulia A, Cabrera Martínez A, Hernández Mira FA, Martin-concepcion P. From Total Roman Domination in Lexicographic Product Graphs to Strongly Total Roman Domination in Graphs. Symmetry (Basel) 2021; 13:1282. [DOI: 10.3390/sym13071282] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Let G be a graph with no isolated vertex and let N(v) be the open neighbourhood of v∈V(G). Let f:V(G)→{0,1,2} be a function and Vi={v∈V(G):f(v)=i} for every i∈{0,1,2}. We say that f is a strongly total Roman dominating function on G if the subgraph induced by V1∪V2 has no isolated vertex and N(v)∩V2≠∅ for every v∈V(G)\V2. The strongly total Roman domination number of G, denoted by γtRs(G), is defined as the minimum weight ω(f)=∑x∈V(G)f(x) among all strongly total Roman dominating functions f on G. This paper is devoted to the study of the strongly total Roman domination number of a graph and it is a contribution to the Special Issue “Theoretical Computer Science and Discrete Mathematics” of Symmetry. In particular, we show that the theory of strongly total Roman domination is an appropriate framework for investigating the total Roman domination number of lexicographic product graphs. We also obtain tight bounds on this parameter and provide closed formulas for some product graphs. Finally and as a consequence of the study, we prove that the problem of computing γtRs(G) is NP-hard.
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38
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Madaras T, Šurimová M. Facial Homogeneous Colouring of Graphs. Symmetry (Basel) 2021; 13:1213. [DOI: 10.3390/sym13071213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
A proper colouring of a plane graph G is called facially homogeneous if it uses the same number of colours for every face of G. We study various sufficient conditions of facial homogeneous colourability of plane graphs, its relation to other facial colourings, and the extension of this concept for embedded graphs in general.
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39
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He B, Langner J, Witek HA. Hexagonal flakes as fused parallelograms: A determinantal formula for
Zhang‐Zhang
polynomials of the
O
(2,
m
,
n
) benzenoids. J CHIN CHEM SOC-TAIP 2021. [DOI: 10.1002/jccs.202000420] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Bing‐Hau He
- Department of Applied Chemistry and Institute of Molecular Science National Chiao Tung University Hsinchu Taiwan
| | - Johanna Langner
- Department of Applied Chemistry and Institute of Molecular Science National Chiao Tung University Hsinchu Taiwan
| | - Henryk A. Witek
- Department of Applied Chemistry and Institute of Molecular Science National Chiao Tung University Hsinchu Taiwan
- Center for Emergent Functional Matter Science National Chiao Tung University Hsinchu Taiwan
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40
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Affiliation(s)
- Özge Çolakoğlu Havare
- Mathematics Department, Arts and Sciences Faculty, Mersin University, Mersin, Turkey
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41
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Li S. On the intrinsic symmetries and parameterization of fullerenes. COMPUT THEOR CHEM 2021. [DOI: 10.1016/j.comptc.2021.113212] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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42
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Nadeem MF, Imran M, Afzal Siddiqui HM, Azeem M, Khalil A, Ali Y. Topological aspects of metal-organic structure with the help of underlying networks. ARAB J CHEM 2021. [DOI: 10.1016/j.arabjc.2021.103157] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
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43
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Witek HA. Zhang-Zhang Polynomials of Multiple Zigzag Chains Revisited: A Connection with the John-Sachs Theorem. Molecules 2021; 26:molecules26092524. [PMID: 33925975 PMCID: PMC8123625 DOI: 10.3390/molecules26092524] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2021] [Revised: 04/09/2021] [Accepted: 04/22/2021] [Indexed: 12/05/2022] Open
Abstract
Multiple zigzag chains Zm,n of length n and width m constitute an important class of regular graphene flakes of rectangular shape. The physical and chemical properties of these basic pericondensed benzenoids can be related to their various topological invariants, conveniently encoded as the coefficients of a combinatorial polynomial, usually referred to as the ZZ polynomial of multiple zigzag chains Zm,n. The current study reports a novel method for determination of these ZZ polynomials based on a hypothesized extension to John–Sachs theorem, used previously to enumerate Kekulé structures of various benzenoid hydrocarbons. We show that the ZZ polynomial of the Zm,n multiple zigzag chain can be conveniently expressed as a determinant of a Toeplitz (or almost Toeplitz) matrix of size m2×m2 consisting of simple hypergeometric polynomials. The presented analysis can be extended to generalized multiple zigzag chains Zkm,n, i.e., derivatives of Zm,n with a single attached polyacene chain of length k. All presented formulas are accompanied by formal proofs. The developed theoretical machinery is applied for predicting aromaticity distribution patterns in large and infinite multiple zigzag chains Zm,n and for computing the distribution of spin densities in biradical states of finite multiple zigzag chains Zm,n.
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Affiliation(s)
- Henryk A. Witek
- Department of Applied Chemistry, Institute of Molecular Science, National Yang Ming Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu 300092, Taiwan;
- Center for Emergent Functional Matter Science, National Yang Ming Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu 300092, Taiwan
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44
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Affiliation(s)
| | - Muhammad Azeem
- Department of Mathematics, COMSATS University Islamabad, Lahore, Pakistan
- Department of Aerospace Engineering, Faculty of Engineering, University Putra Malaysia, Malaysia
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45
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Zhao D, Chu YM, Siddiqui MK, Ali K, Nasir M, Younas MT, Cancan M. On Reverse Degree Based Topological Indices of Polycyclic Metal Organic Network. Polycycl Aromat Compd 2021. [DOI: 10.1080/10406638.2021.1891105] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Dongming Zhao
- School of Automation, Wuhan University of Technology, Wuhan, P.R. China
| | - Yu-Ming Chu
- Department of Mathematics, Huzhou University, Huzhou, P.R. China
- Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha, P.R. China
| | | | - Kashif Ali
- Department of Mathematics, COMSATS University Islamabad, Lahore, Pakistan
| | - Muhammad Nasir
- Department of Mathematics, COMSATS University Islamabad, Lahore, Pakistan
| | | | - Murat Cancan
- Faculty of Education, Van Yuzuncu Yil University, Van, Turkey
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46
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Hayat S, Khan S. Quality testing of spectrum-based valency descriptors for polycyclic aromatic hydrocarbons with applications. J Mol Struct 2021; 1228:129789. [DOI: 10.1016/j.molstruc.2020.129789] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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47
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Wei J, Cancan M, Rehman AU, Siddiqui MK, Nasir M, Younas MT, Hanif MF. On Topological Indices of Remdesivir Compound Used in Treatment of Corona Virus (COVID 19). Polycycl Aromat Compd 2021. [DOI: 10.1080/10406638.2021.1887299] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Affiliation(s)
- Jianxin Wei
- School of Mathematics and Statistics Science, Ludong University, Yantai, Shandong, 264025, China
| | - Murat Cancan
- Faculty of Education, Van Yuzuncu Yil University, Van, Turkey
| | - Atiq Ur Rehman
- Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
| | | | - Muhammad Nasir
- Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
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48
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Abstract
A double Roman dominating function on a graph G=(V,E) is a function f:V→{0,1,2,3} with the properties that if f(u)=0, then vertex u is adjacent to at least one vertex assigned 3 or at least two vertices assigned 2, and if f(u)=1, then vertex u is adjacent to at least one vertex assigned 2 or 3. The weight of f equals w(f)=∑v∈Vf(v). The double Roman domination number γdR(G) of a graph G is the minimum weight of a double Roman dominating function of G. A graph is said to be double Roman if γdR(G)=3γ(G), where γ(G) is the domination number of G. We obtain the sharp lower bound of the double Roman domination number of generalized Petersen graphs P(3k,k), and we construct solutions providing the upper bounds, which gives exact values of the double Roman domination number for all generalized Petersen graphs P(3k,k). This implies that P(3k,k) is a double Roman graph if and only if either k≡0 (mod 3) or k∈{1,4}.
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Sharoyko VV, Ageev SV, Podolsky NE, Petrov AV, Litasova EV, Vlasov TD, Vasina LV, Murin IV, Piotrovskiy LB, Semenov KN. Biologically active water-soluble fullerene adducts: Das Glasperlenspiel (by H. Hesse)? J Mol Liq 2021; 323:114990. [DOI: 10.1016/j.molliq.2020.114990] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
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50
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Chu Y, Siddiqui MK, Javed S, Sherin L, Kausar F. On Zagreb Type Molecular Descriptors of Ceria Oxide and Their Applications. J CLUST SCI 2022; 33:537-46. [DOI: 10.1007/s10876-021-01984-y] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
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