Hamming index of product graphs

Let [Formula: see text] be a simple graph of order [Formula: see text]. The adjacency matrix of [Formula: see text] is a square matrix of order [Formula: see text], whose elements are [Formula: see text], if the corresponding vertices are adjacent and [Formula: see text], if the corresponding vertices are non-adjacent. Each row of the adjacency matrix is called as a string. The Hamming distance between two strings [Formula: see text] and [Formula: see text] 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.