Topological aspects of 2D structures of trans- Pd(NH2)S lattice and a metal-organic superlattice

Entropy analysis of nickel(II) porphyrins network via curve fitting techniques

Nickel(II) porphyrins typically adopt a square planar coordination geometry, with the nickel atom located at the center of the porphyrin ring and the coordinating atoms arranged in a square plane. The additional atoms or groups coordinated to the nickel atom in nickel(II) porphyrins are called ligands. Porphyrins have been investigated as potential agents for imaging and treating cancer due to their ability to selectively bind to tumor cells and be used as sensors for a variety of analytes. Nickel(II) porphyrins are relatively stable compounds, with high thermal and chemical stability. They can be stored in a solid state or in solution without significant degradation. In this study, we compute several connectivity indices, such as general Randi'c, hyper Zagreb, and redefined Zagreb indices, based on the degrees of vertices of the chemical graph of nickel porphyrins. Then, we compute the entropy and heat of formation NiP production, among other physical parameters. Using MATLAB, we fit curves between various indices and the thermodynamic properties parameters, notably the heat of formation and entropy, using various linearity- and non-linearity-based approaches. The method's effectiveness is evaluated using [Formula: see text], the sum of squared errors, and root mean square error. We also provide visual representations of these indexes. These mathematical frameworks might offer a mechanism to investigate the thermodynamical characteristics of NiP's chemical structure under various circumstances, which will help us understand the connection between system dimensions and these metrics.

On Entropy Measures and Eccentricity-Based Descriptors of Polyamidoamine (PAMAM) Dendrimers

Topological indices (TIs) assign a numeric value to a graph or a molecular structure. Due to their ability to predict the physiochemical properties of a molecular graph, several TIs have been introduced and studied, mainly based on degree and distance. For a vertex $v$ , the maximum distance of $v$ from any other vertex in a graph $G$ is called the eccentricity of $v$ , which is denoted by $\sigma \left(v\right)$ , in $G$ . The eccentricity of vertices gained special attention among the distance-based or degree-distance based TIs. An important TI in the class of eccentricity-dependent TIs is an eccentricity-entropy index. Furthermore, other eccentricity-dependent TIs such as eccentric-connectivity index, total-eccentricity index, and the first Zagreb index have also been extensively studied. On the other hand, dendrimers came out as unique polymeric macromolecules because of extensively branched three-dimensional architectural characteristics. This structure design prepares for various unique properties of dendrimers, including monodispersity, multivalency, uniform size, globular shape, water solubility with hydrophobic internal cavities, and a high degree of branching. These properties make them attractive candidates for different applications. PAMAM (polyamidoamine) dendrimers are promising polymers that can be successfully used in various biomedical applications. The PAMAM dendrimers having different structures such as a primary amine as the end group or porphyrin core have been studied through graph-theoretic parameters. This paper studies these two types of PAMAM dendrimers through eccentricity-dependent parameters. In particular, we establish formulae of eccentricity entropy for two types of PAMAM dendrimers. Moreover, we also derive analytic formulae of some other significant TIs from the class of eccentricity-dependent TIs. Furthermore, we apply graphical tools to demonstrate the trends of the values in the obtained results.

Treatment of COVID-19 Patients Using Some New Topological Indices

COVID-19 is causing havoc to human health and the world economy right now. It is a single standard positive-sense RNA virus which is transferred by inhalation of a viral droplet. Its genome forms four structural proteins such as nucleocapsid protein, membrane protein, spike protein, and envelop protein. The capsid of coronavirus is a protein shell within which a positive strand of RNA is present which enables the virus to control the machinery of human cells. It has several variants, e.g., SARS, MERS, and now a new variant identified in 2019, which is a novel coronavirus that causes novel coronavirus disease (COVID-19). COVID-19 is a novel coronavirus disease that originally arose in Wuhan, China, and quickly spread around the world. Clinically, we identified the virus presence by a PCR-based test. Preventive measures and vaccination are the only treatment against coronavirus. Some of these include Remdesivir (GS-5734), Chloroquine, Hydroxychloroquine, and Theaflavin. A topological index (TI) is a mathematical function that assigns a numerical value to a (molecular) graph and predicts many physical, chemical, biological, thermodynamical, and structural features of that network. In this work, we will calculate a new topological index, namely, the first and second Gourava and Hyper-Gourava indices for the molecular graph of Remdesivir (GS-5734), Chloroquine, Hydroxychloroquine, and Theaflavin. We also plotted our computed results to examine how they were affected by the parameters involved. These findings could contribute in the development of new COVID-19 therapy options.

Computation of M-Polynomial and Topological Indices of Phenol Formaldehyde

Phenol formaldehyde (phenolic resin) has a wide range of moldings. However, it has immense consumption in manufacturing electrical equipment due to its insulating property. Phenolic resin retains properties at the freezing point, and also its age cannot be determined. Due to its insulator property, it has wide use in electrical equipment. In this article, degree-based topological indices of phenol formaldehyde are determined with the help of M-polynomial. We calculate the Zagreb index, Randić index, K-Banhatti indices, modified K-Banhatti indices, atom-bond connectivity index, geometric arithmetic index, symmetric index, inverse sum index, and harmonic index.

Topological Attributes of Silicon Carbide Si C 4 - II i , j Based on Ve-Degree and Ev-Degree

The study of graphs containing edges and nodes is of great importance in science and in real life. Topological indices $\left(\text{TIs}\right)$ are numerical parameters linked to chemical graphs used to estimate the biological, toxicological, and physical properties of chemical compounds. Recently, two terms, ev-degree- and ve-degree-based TIs, have been defined in chemical graph theory. In this paper, we have estimated degree-based TIs, namely, ev-degree Zagreb $\left(\text{M}\right)$ type index, ev-degree Randic $\left(\text{R}\right)$ index, ve-degree atom-bond connectivity $\left(\text{ABC}\right)$ index, ve-degree geometric arithmetic index $\left(\text{GA}\right)$ , ve-degree harmonic $\left(\text{H}\right)$ index, and ve-degree sum-connectivity index for $\text{Si}{\text{C}}_4$ - $\text{II}\left[i,j\right]$ .

Molecular Descriptors on Line Graphs of Cactus Chains and Rooted Products Graphs

The application of graph theory in the study of molecular physical and chemical properties involves theoretical mathematical chemistry. Atoms, represented by vertices, and edges, represented by bonds between them, are detailed in simple graphs called chemical graphs. The mathematical derivation of the numerical value of a graph is called the molecular descriptor of the graph. Any connected graph wherein no edge is contained in exclusive of a single cycle is called a cactus graph. In the research in this article, expressions for various molecular descriptors of line graph of the graph obtained by the rooted product of the cycle and path graphs are constructed. This article obtained the calculation of molecular descriptors for line graphs of chain ortho cactus and chain para cactus graphs. To predict the biological activity of a compound, the generalized Zagreb index, the first Zagreb index $M_1\left(G\right)$ , the second Zagreb index $M_2\left(G\right)$ , the F-index, the general Randic index, the symmetric division, the atom bond connectivity (ABC), and the geometric arithmetic (GA) descriptors are created.

A Paradigmatic Approach to Find Equal Sum Partitions of Zero-Divisors via Complete Graphs

In computer science and mathematics, a partition of a set into two or more disjoint subsets with equal sums is a well-known NP-complete problem. This is a hard problem and referred to as the partition problem or number partitioning. In this paper, we solve a particular type of NP-complete problem on the set of all zero-divisors of $Z_n$ including zero, where $Z_n$ is the ring of residue classes of a positive integer $n$ . In this regard, we introduce and investigate quadratic zero-divisor graph in which we build an edge between zero-divisors $z_i$ and $z_j$ if and only if $z_i^2\equiv z_j^2\left(\mathrm{mod}n\right),i\ne j$ . This is denoted as $\overbrace{G}\left(2,n\right)$ . We characterize these graphs in term of complete graphs for classes of integers $2^{\alpha },p^{\alpha },2^{\alpha }p,2p^{\alpha }$ and $pq$ , where $\alpha$ is any positive integer and $p,q$ are odd primes.

Degree-Based Molecular Descriptors of Guar Gum and Its Chemical Derivatives

The most abundant polycarbonates that are found in food are polysaccharides. A long chain of monosaccharide with glycosidic linkages forms polymeric carbohydrates. These carbohydrates with water in the process of hydrolysis produces sugar monosaccharides or oligosaccharides. The examples of polysaccharides include starch, galactogen, and glycogen. They contribute various applications mainly in food storage, pharmaceutical industry, and petroleum extraction. In this work, a polysaccharide known as guar gum is studied and also ten degree-based topological indices, namely, Zagreb indices, Randic index, general Randic index, forgotten index, ABC index, GA index, GH index, Sombor index, and SS index are computed. The chemical derivatives of guar gum such as HPG, CMG, and CMHPG are studied, and topological indices are determined. Finally, numerical and graphical comparison of all the above said ten indices are made for guar gum and its chemical derivatives.