Investigation molecular structure of anticancer drug with topological indices.

A crucial consideration in examining the physicochemical characteristics of chemical compound structures is topological indices. In addition, topological indices will serve as a description of a molecule under test by translating each molecule's structure into a real number. In this paper, we calculate topological indices [Formula: see text] and [Formula: see text] for anticancer drugs, where da is the degree of vertex a in graph G and 0≠α,ß∈R. By choosing of parameters α and ß, some of new/old results for topological indices are obtained. The results of this study may assist to chemists in identifying the chemical, physical and biological activity associated with them.

The study of pentagonal chain with respect to schultz index, modified schultz index, schultz polynomial and modified schultz polynomial.

Distance-based topological indices are numerical parameters that are derived from the distances between atoms in a molecular structure, and they provide a quantitative measure of the topology and geometry of a molecule. The distance-based topological indices uses to predict various properties of molecules, including their boiling points, melting points, and solubility. It also predicts the biological activity of molecules, including their pharmacological and toxicological properties. Pentagonal chain molecules are organic compounds that consist of a linear chain of five-membered (pentagons) connected by carbon and bonds. These molecules have unique structural and electronic properties that make them useful in a variety of applications. Motivated by the pentagonal chain molecules, we have considered a pentagonal chain graph and it is denoted by Pn. We have computed some distance based topological indices for Pn. The paper focuses on a pentagonal chain molecules denoted by G, and derives several distance-based topological indices. These indices compromise insights into physicochemical properties, aid in identifying structural characterizations, and enhance understanding of molecular properties.

Multiple-Criteria Decision-Making (MCDM) techniques to study the behavior of dendrimers using topological indices.

Topological indices provide a mathematical language for capturing molecular structure, symmetry, and predicting properties. Dendrimers are microscopic bilaterally symmetrical molecules with a well-defined homogeneous nanoparticles structure, often consisting of a symmetric center, inner shell, and outer shell. In this work, first we compute some degree-based topological indices of Porphyrin (DnPn),Poly (Propyl) Ether Imine(PETIM), Zinc porphyrin (DPZn), and Polyamidoamine (PAMAM) dendrimers. Then, we use multi-criteria decision making (MCDM) techniques to establish the weighted evaluation of dendrimer classes based on certain topological indices. For weighted analysis we correlate the properties of benzene derivatives with topological invariants. Finally, based on the multi-criteria decision making techniques namely TOPSIS, SAW and MOORA method, we have ranked the dendrimer structures based on their properties.

Some inequalities for two simplices in the Euclidean space En.

Simplices are used as building blocks to construct an interesting class of topological spaces called simplicial complexes, which exhibit remarkable symmetric properties. In this paper, we study the problems of inequalities for two simplices in the Euclidean space En. We establish some new inequalities for the vertex distances of two simplices and obtain some generalizations of the classical Neuberg-Pedoe inequality.

On Some Topological Indices Defined via the Modified Sombor Matrix.

Let G be a simple graph with the vertex set V={v1,…,vn} and denote by dvi the degree of the vertex vi. The modified Sombor index of G is the addition of the numbers (dvi2+dvj2)-1/2 over all of the edges vivj of G. The modified Sombor matrix AMS(G) of G is the n by n matrix such that its (i,j)-entry is equal to (dvi2+dvj2)-1/2 when vi and vj are adjacent and 0 otherwise. The modified Sombor spectral radius of G is the largest number among all of the eigenvalues of AMS(G). The sum of the absolute eigenvalues of AMS(G) is known as the modified Sombor energy of G. Two graphs with the same modified Sombor energy are referred to as modified Sombor equienergetic graphs. In this article, several bounds for the modified Sombor index, the modified Sombor spectral radius, and the modified Sombor energy are found, and the corresponding extremal graphs are characterized. By using computer programs (Mathematica and AutographiX), it is found that there exists only one pair of the modified Sombor equienergetic chemical graphs of an order of at most seven. It is proven that the modified Sombor energy of every regular, complete multipartite graph is 2; this result gives a large class of the modified Sombor equienergetic graphs. The (linear, logarithmic, and quadratic) regression analyses of the modified Sombor index and the modified Sombor energy together with their classical versions are also performed for the boiling points of the chemical graphs of an order of at most seven.

Theoretical Study of Ability of Boron Nitride Nanocone to Oxidation of Sulfur Monoxide.

In recent years, the discovery of suitable catalyst to oxidation of sulfur monoxide (SO) in normal temperature is a major concern in the industry. In this study, in first step; the boron nitride nanocone (BNNC) with Ge were doped and the surface of Ge-BNNC by using of the O2 molecule were activated. In second step; oxidation of SO on surface of Ge-BNNC through the Langmuir Hinshelwood (LH) and Eley Rideal (ER) mechanisms was investigated. Calculated data reveal that surface of O2-Ge-BNNC oxide the SO molecule with Ge-BNNC-O-O* + SO → Ge-BNNC-O-O*-SO → Ge-BNNC-O* + SO2 and Ge-BNNC-O* + SO → Ge-BNNC + SO2 reactions. It can be concluded, the energy barrier of LH mechanism to oxidation of SO on Ge-BNNC is lower than ER mechanism. Finally, the Ge-BNNC is acceptable catalyst with low price and high performance to oxidation of SO in normal temperature.