Hosoya, Schultz, Modified Schultz Polynomials and Their Topological Indices of Benzene Molecules: First Members of Polycyclic Aromatic Hydrocarbons (PAHs)

A topological index is a real number related to the structure of a connected graph G and is invariant under graph automorphism. Let G be a (molecular) graph possessing n vertices and m edges, and e=x,y be an edge of G and x, y are two of its vertices, then the distance d(x,y)=d(x,y|G) between the vertices x and y is equal to the length of the shortest path that connects them in G. The goal of this paper is to compute the Schultz Polynomial     ( , ) {u,v} V G 1 G,x ( ) , 2 d u v u v Sc d d x     Modified Schultz Polynomial     * ( , ) {u,v} V G 1 G,x ( ) , 2 d u v u v Sc d d x    Hosoya Polynomial       d v,u { , } V G 1 G,x x 2 u v H    and their topological indices of first members of a family of hydrocarbon structures “Polycyclic Aromatic Hydrocarbons (PAHs)” molecular graph. Copyright © acascipub.com, all rights reserved.