Hamming index of product graphs

Let G be a simple graph of order n. The adjacency matrix of G is a square matrix of order n, whose elements are 1, if the corresponding vertices are adjacent and 0, if the corresponding vertices are non-adjacent. Each row of the adjacency matrix is called as a string. The Hamming distance between two strings s1 and s2 is the number of positions at which their values differ. The sum of Hamming distances between each pair of vertices is the Hamming index of underlying graph. In this paper, the Hamming indices of different product graphs are obtained.