Wiener and hyper–wiener indices of unitary addition cayley graphs

Abstract

A topological index is a number associated to a graph. In chemical graph theory the Wiener index of a graph G, denoted by W(G) is the sum of the distance between all (unordered) pairs of vertices of G. That is, (Formula Presented), where d (ui, uj) is the shortest distance between the vertices. ui and uj. The Hyper-Wiener Index WW(G) is the generalization of the Wiener index. The Hyper-Wiener Index of a graph G is, (Formula Presented). The unitary addition Cayley graph Gn has a vertex set Zn = {0, 1,…, n-1} and the vertices u and v are adjacent if gcd (u+v,n) =1. In this paper Wiener index and Hyper Wiener indices of Unitary addition Cayley graph Gn is computed.