Vertex Szeged indices of P_2n + _F P_n+1

Abstract

Let G=(V,E) be a simple connected graph, where V(G) and E(G) represent the vertex set and edge set of G respectively. For a graph the vertex Szeged index is equal to the product over all edges uv of G of the number of vertices which are not equidistant to vertices u and v. The vertex Padmarker-Ivan (PIv) index of a graph is the sum over all edges uv of G of the number of vertices which are not equidistant to vertices u and v. The aim of this paper is to compute and compare the vertex Szeged index and vertex Padmarker-Ivan (PIv) index of P2n+F Pn+1, where P2n+FPn+1 represents four operation on P2n×Pn+1.