Comparative Study of Zagreb Indices for Capped, Semi-Capped, and Uncapped Carbon Nanotubes

Applications of magnesium iodide structure via modified-polynomials

A relatively recent approach in molecular graph theory for analyzing chemical networks and structures is called a modified polynomial. It emphasizes the characteristics of molecules through the use of a polynomial-based procedure and presents numerical descriptors in algebraic form. The Quantitative Structure-Property Relationship study makes use of Modified Polynomials (M-Polynomials) as a mathematical tool. M-Polynomials used to create connections between a material's various properties and its structural characteristics. In this study, we calculated several modified polynomials and gave a polynomial description of the magnesium iodide structure. Particularly, we computed first, second and modified Zagreb indices based M-polynomials. Randić index, and inverse Randić indices based M-polynomials are also computed in this work.

Connection number topological aspect for backbone DNA networks

The present study investigates the complex topological characteristics of DNA networks, with a specific emphasis on the innovative metric known as Connection Number (CN) as a key factor in determining network structure. The Connection Number, represented as CN(v) for a vertex v, measures the count of unique paths that link v to every other vertex in the network. By employing rigorous mathematical modeling and analysis techniques, we are able to reveal the profound implications of CN (complex networks) in characterizing the structural robustness and dynamics of information flow within DNA networks. The study of how the theory of graphs and chemicals interact is known as chemical graph theory. This paper, computing the hyper Zagreb connection index, augmented connection index, inverse sum connection index, harmonic connection index, symmetric division connection index, geometric arithmetic connection index, and atom bond connectivity connection index, of two significant types of backbone DNA and Barycentric subdivision of backbone DNA networks. Direct method computation is used to produce these Connection-based topological descriptors.

Chemical applicability and computation of K-Banhatti indices for benzenoid hydrocarbons and triazine-based covalent organic frameworks

The novel applications in chemistry include the mathematical models of molecular structure of the compounds which has numerous findings in this area that refers to mathematical chemistry. Topological descriptors play a major role in QSAR/QSPR studies that analyses the biological and physicochemical properties of the compounds. In the recent times, a new type of topological descriptors are proposed, called K-Banhatti indices. In this study the chemical applicability of K-Banhatti indices are examined for benzenoid hydrocarbons (derivatives of benzene). These indices have shown remarkable results through the study of statistical analysis. Subsequently, triazine-based covalent organic frameworks (CoF's) are studied for which [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and HB(G) of a graph G are computed.

Sombor topological indices for different nanostructures

Euclidean geometry is utilized to establish the Sombor graph parameter and its invariants. It is sum of all adjacent vertices in graph theory d ϒ 2 + d Γ 2 where d ϒ is the degree of the vertex ϒ. Geometrical interpretation is used to describe the new Sombor indices types. We examined, recently developed Sombor indices for various nanotube Y-junctions in this article. In specifically, the first area-based Sombor index was introduced by Euclidean geometry. Angular orientation concept to construct the second, fourth, and sixth Sombor graph parameters, while third and fifth Sombor graph parameters are constructed by perimeter.

Some new results on the face index of certain polycyclic chemical networks

Silicate minerals make up the majority of the earth's crust and account for almost 92 percent of the total. Silicate sheets, often known as silicate networks, are characterised as definite connectivity parallel designs. A key idea in studying different generalised classes of graphs in terms of planarity is the face of the graph. It plays a significant role in the embedding of graphs as well. Face index is a recently created parameter that is based on the data from a graph's faces. The current draft is utilizing a newly established face index, to study different silicate networks. It consists of a generalized chain of silicate, silicate sheet, silicate network, carbon sheet, polyhedron generalized sheet, and also triangular honeycomb network. This study will help to understand the structural properties of chemical networks because the face index is more generalized than vertex degree based topological descriptors.

Breast cancer chemical structures and their partition resolvability

Cancer is a disease that causes abnormal cell formation and spreads throughout the body, causing harm to other organs. Breast cancer is the most common kind among many of cancers worldwide. Breast cancer affects women due to hormonal changes or genetic mutations in DNA. Breast cancer is one of the primary causes of cancer worldwide and the second biggest cause of cancer-related deaths in women. Metastasis development is primarily linked to mortality. Therefore, it is crucial for public health that the mechanisms involved in metastasis formation are identified. Pollution and the chemical environment are among the risk factors that are being indicated as impacting the signaling pathways involved in the construction and growth of metastatic tumor cells. Due to the high risk of mortality of breast cancer, breast cancer is potentially fatal, more research is required to tackle the deadliest disease. We considered different drug structures as chemical graphs in this research and computed the partition dimension. This can help to understand the chemical structure of various cancer drugs and develop formulation more efficiently.

Comparative study of vertex-edge based indices for semi-capped carbon nanotubes

Manufacturing relatively inexpensive items in every area of engineering and science is the major focus of exploration resultant the world's contemporary economic setback. Making small-sized items that are inexpensive and lightweight while providing high quality is critical in today's and tomorrow's worlds. Nanotechnology has a significant role to play in this situation. Nano-objects or, in general, nanomaterials are especially preferred; nanotubes, especially those comprised of carbon, are one of the most popular types of nanostructures, and they are applied in a variety of chemical, biological and technical applications. This notion prompted us to investigate their many physical and chemical characteristics. We utilized topological descriptors to evaluate diverse nanotube structures such as armchair carbon and semi-capped nanotubes by using vertex-edge based indices to characterize distinct chemical structures via numerical quantitative analysis. Furthermore, we examined uncapped and semi-capped armchair carbon nanotubes and achieved adequate comparative findings.

Partition dimension of COVID antiviral drug structures

In November 2019, there was the first case of COVID-19 (Coronavirus) recorded, and up to 3$ ^{rd }$ of April 2020, 1,116,643 confirmed positive cases, and around 59,158 dying were recorded. Novel antiviral structures of the SARS-COV-2 virus is discussed in terms of the metric basis of their molecular graph. These structures are named arbidol, chloroquine, hydroxy-chloroquine, thalidomide, and theaflavin. Partition dimension or partition metric basis is a concept in which the whole vertex set of a structure is uniquely identified by developing proper subsets of the entire vertex set and named as partition resolving set. By this concept of vertex-metric resolvability of COVID-19 antiviral drug structures are uniquely identified and helps to study the structural properties of structure.

Minimum Zagreb Eccentricity Indices of Two-Mode Network with Applications in Boiling Point and Benzenoid Hydrocarbons

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.

Mostar Index of Cycle-Related Structures

A topological index is a numerical quantity associated with the molecular structure of a chemical compound. This number remains fixed with respect to the symmetry of a molecular graph. Diverse research studies have shown that the topological indices of symmetrical graphs are interrelated with several physiochemical properties such as boiling point, density, and heat of formation. Peripherality is also an important tool to study topological aspects of molecular graphs. Recently, a bond-additive topological index called the Mostar index that measures the peripherality of a graph is investigated which attained wide attention of researchers. In this article, we compute the Mostar index of cycle-related structures such as the Jahangir graph and the cycle graph with chord.

Analysis of Dendrimer Generation by Sombor Indices

Dendrimers are highly branched, star-shaped macromolecules with nanometer-scale dimensions. Dendrimers are defined by three components: a central core, an interior dendritic structure (the branches), and an exterior surface with functional surface groups. Topological indices are numerical numbers that help us to understand the topology of different dendrimers and can be used to predict the properties without performing experiments in the wet lab. In the present paper, we computed the Sombor index and the reduced version of the Sombor index for the molecular graphs of phosphorus-containing dendrimers, porphyrin-cored dendrimers, PDI-cored dendrimers, triazine-based dendrimers, and aliphatic polyamide dendrimers. We also plotted our results by using Maple 2015 which help us to see the dependence of the Sombor index and reduced Sombor index on the involved parameters. Our results may help to develop better understanding about phosphorus-containing dendrimers, porphyrin-cored dendrimers, PDI-cored dendrimers, triazine-based dendrimers, and aliphatic polyamide dendrimers. Our results are also useful in the pharmaceutical industry and drug delivery.