Analysis of Some Topological Indices at Distance$-2$ of  Carbon Nanosheet $HC_5C_7[h,c]$

Abstract

Topological indices defined for the molecular graphs by  Gutman and Trinajstić are based on the degree of the vertices which are at distance one. Analogous to this, the generalized  topological indices based on the degree of the vertices which are at the distance $1\le l\le diam (G)$ is introduced. This extension aims to provide a more comprehensive understanding of the molecular structure, offering insights into the connectivity patterns beyond immediate neighbors. The study contributes to the exploration of advanced topological measures, potentially enhancing the characterization of complex structures. In this work, a general formula for some important degree-based indices based on distance-2 of the vertices for a 2 dimension latices of $HC_5C_7$ nanosheet is determined. These indices help in predicting physicochemical properties without the involvement of the laboratory. Also, a visual comparison of these indices are shown.