Hamming distance between the strings generated by adjacency matrix of a subgraph complementary graph and their sum

Abstract

Let [Formula: see text] be the adjacency matrix of a graph [Formula: see text]. Let [Formula: see text] denote the row entries of [Formula: see text] corresponding to the vertex [Formula: see text] of [Formula: see text]. The Hamming distance between the strings [Formula: see text] and [Formula: see text] is the number of positions in which [Formula: see text] and [Formula: see text] differ. In this paper, we study the Hamming distance between the strings generated by the adjacency matrix of subgraph complement of a graph. We also compute sum of Hamming distances between all pairs of strings generated by the adjacency matrix of [Formula: see text].