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

#### Abstract

Let \(A(G)\) be the adjacency matrix of a graph \(G\). Denote by \(s(v)\) the row of the adjacency matrix corresponding to the vertex \(v\) of \(G\). It is a string in the set \({\Bbb Z}_2^n\) of all \(n\)-tuples over the field of order two. The Hamming distance between the strings \(s(u)\) and \(s(v)\) is the number of positions in which \(s(u)\) and \(s(v)\) differ. In this paper the Hamming distance between the strings generated by the adjacency matrix is obtained. Also \(H_A(G)\), the sum of the Hamming distances between all pairs of strings generated by the adjacency matrix is obtained for some graphs.

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