The Schultz and modified Schultz polynomials of certain subdivision and line subdivision graphs

Mohammad Reza Farahani and Muh

Abstract

For a connected graph G(V(G),E(G)), du and d(u,v) represents the degree of u and the distance between u and v. Ivan Gutman defined the Schultz and modified Schultz polynomials as ( , ) { , } ( ) ( , ) ( ) d u v u v u v V G Sc G x d d x Í = Σ + and ( , ) { , } ( ) *( , ) d u v u v u v V G Sc G x d d x Í = Σ , respectively. Such that their first derivative at x=1 are equal to { , } ( ) ( ) ( ) ( , ) u v u v V G Sc G d d d u v Í = Σ + and { , } ( ) *( ) ( ) ( , ) u v u v V G Sc G d d d u v Í = Σ , respectively, which are the Schultz index and its modification. In this paper, we compute the Schultz and modified Schultz polynomials and their corresponding indices of the subdivision graph and the line graph subdivision graph of wheel graph