Schultz and Modified Schultz Polynomials for Edge – Identification Chain and Ring – for Pentagon and Hexagon Graphs

Abstract

Abstract In a connected graph G, the distance function between each pair of two vertices from a set vertex V(G) is a shortest distance between them and the vertex degree v, deg v, is the number of edges which are incident to the vertex v. The Schultz and modified Schultz polynomials of G are have defined as :Sc(G; x) = ∑( deg v + deg u) x d (u, v) and Sc ∗ (G; x) = ∑ (deg v. deg u) x d (u, v), respectively, where the summations are taken over all unordered pairs of distinct vertices in V(G) and d(u, v) is the distance between u and v in V(G). We shall find the general forms of Schultz and modified Schultz polynomials and indices of the edge – identification chain and ring – pentagon and hexagon graphs in the present work.