Jayjit Barman

Silicon carbide, often known as carborundum, is a combination of silicon and carbon. Silicon carbide is one semiconductor material that is increasingly being utilized in semiconductor devices. In 1...

The numerical values extracted from a graph that indicates its topology are called topological indices. A contemporary and efficient method is to compute a graph's topological indices using the graph polynomial that corresponds to it. This method of identifying degree-based topological indices involves the use of the M-polynomial. Very recently, in 2025, the hyperbolic Sombor index (HSO) was proposed and shows its chemical applicability for octane isomers and the structure sensitivity and abruptness for octane, nonane, and decane isomers, respectively. In this work, we establish the closed derivation formula for the above-mentioned index of a graph based on its M-polynomial. Additionally, we use our proposed derivation formula to calculate the hyperbolic Sombor index of a few standard graphs and chemical families. Moreover, we provide the numerical and graphical representations for the M-polynomial and the computed HSO index of the chemical families.

A topological index is a numerical value that correlates with a chemical structure. A degree-based topological index of drug molecular structures

This article presents a new geometric approach to forming molecular structure descriptors (topological indices) based on vertex degrees. The degrees of a pair of adjacent vertices are represented by the length of the semi-major and semi-minor axes of the hyperbola that form the basis of the model. In this way, a number of previously known topological indices can now be interpreted geometrically and some new topological indices can be generated. The eccentricity of the hyperbola gives rise to a remarkably simple vertex-degree-based topological index, which we refer to as the hyperbolic Sombor index (HSO). We concentrate on some of the most important properties of this index, such as prediction power, structure sensitivity and degeneracy. We apply statistical approaches and computing methods to the octane, nonane and decane isomer data sets to compare these properties with other well-known degree-based topological indices.