Hamming Matrix and Hamming Energy of a Graph

Abstract

Hamming distance is a highly valuable quantity in computer science. In this work, we establish the Hamming matrix H of a graph G, H(G). This is a square matrix, where the elements of the H(G) are Hamming distances. Also, we define the Hamming energy of a graph, HE(G), which is a sum of the absolute eigenvalues of H(G). Finally, we present some bounds on the HE(G) and its predictive potential.