HAMMING DISTANCE BETWEEN THE STRINGS GENERATED BY ADJACENCY MATRIX OF GENERALISED COMPLEMENTS OF A GRAPH AND THEIR SUM
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Let A(G) be the adjacency matrix of a graph G. Let s(v) denote the row entries of A(G) corresponding to the vertex v of G. 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, we study the Hamming distance between the strings generated by the adjacency matrix of generalised complements of a graph. We also compute sum of Hamming distances between all pairs of strings generated by the adjacency matrix of GPk and GP k(i).
Abstract
Let A(G) be the adjacency matrix of a graph G. Let s(v) denote the row entries of A(G) corresponding to the vertex v of G. 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, we study the Hamming distance between the strings generated by the adjacency matrix of generalised complements of a graph. We also compute sum of Hamming distances between all pairs of strings generated by the adjacency matrix of GPk and GP k(i).
참고문헌 (5)
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- E. Sampathkumar, "Generalized complements of a graph", Indian J. Pure Appl. Math, 29, pp.625~639 (1998)