Geodesic
Hamming distance between the strings generated by adjacency matrix of a graph and their sum
Algebra and discrete mathematics, Tome 22 (2016) no. 1, pp. 82-93

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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 $\mathbb{Z}_2^n$ 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.
Keywords: Hamming distance, string, adjacency matrix. 
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     title = {Hamming distance between the strings generated by adjacency matrix of a graph and their sum},
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Asha B. Ganagi; Harishchandra S. Ramane. Hamming distance between the strings generated by adjacency matrix of a graph and their sum. Algebra and discrete mathematics, Tome 22 (2016) no. 1, pp. 82-93. http://geodesic.mathdoc.fr/item/ADM_2016_22_1_a4/