Spectral radius of the Harary matrix of the join product of regular graphs1

Abstract

Abstract The distance between two vertices is equal to the number of edges on the shortest path connecting them. The Harary matrix of a simple, undirected, connected and unweighted graph of n vertices is an nonnegative matrix of order n, such that the (i, j)-entry is equal to the reciprocal distance between the vertices vi and Vj if the vertices are different and zero if are equal. In this work we found bounds for the spectral radius of the Harary matrix of the join product of regular graphs.