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 dϒ2+dΓ2 where dϒ 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.

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.

Several Zagreb indices of power graphs of finite non-abelian groups.

Molecular topology can be described by using topological indices. These are quantitative measures of the essential structural features of a proposed molecule calculated from its molecular structure. It is a numerical value obtained from a molecular configuration that reflects the significant physical characteristics of the suggested molecule. Numerous physical properties, chemical reactivity, and biological activity are correlated with the chemical composition using an algebraic number. The power graph P(G) of a finite group G is a graph whose vertex set is G and in which two distinct vertices are connected by an edge when one element is an integral power of the other. This article investigates a wide range of degree-based topological descriptors for power graphs of various finite groups. We find numerous Zagreb indices (given in Table 1) of power graphs of finite non-cyclic and cyclic groups, dihedral, and generalized quaternion groups.

Computational analysis for eccentric neighborhood Zagreb indices and their significance.

In this paper, a novel eccentric neighborhood degree-based topological indices, termed eccentric neighborhood Zagreb indices, have been conceptualized and its discriminating power investigated with regard to the predictability of the boiling point of the chemical substances. The discriminating power of the eccentric neighborhood Zagreb indices was compared with that of Wiener and eccentric connectivity indices. Some explicit results for those new indices for some graphs and graph operations such as join, disjunction, composition, and symmetric difference.

A novel perspective for M-polynomials to compute molecular descriptors of borophene nanosheet.

Nanomaterials feature exceptional, one-of-a-kind qualities that might be used in electronics, medicine, and other industries. Two-dimensional nanomaterials called borophene have a variety of intriguing characteristics, which helped them to leave an indelible impression in the fields of chemistry, material science, nanotechnology, and condensed matter physics. The concept of modelling the structure of a molecule or chemical network to a chemical graph and then quantitatively analysing them with the aid of topological descriptors was a major advance in the fields of mathematics and chemistry, with a wide range of applications. M-polynomial approach is a very versatile and quick method for computing the degree-based descriptors of chemical graphs or networks. The degree-based descriptors of the [Formula: see text]-Borophene nanosheet are established in this study utilising the M-polynomial technique. A program code that enables to generate the M-polynomial of any chemical structure was developed in Java platform and the same is displayed. At the conclusion, the numerical and graphical comparison based on the identified analytic expressions is also provided. Additionally, the QSPR analysis was also carried out and the outcoms are presented therein.