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Algebra and Discrete Mathematics, 2016, Volume 22, Issue 1, Pages 82–93
(Mi adm575)
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RESEARCH ARTICLE
Hamming distance between the strings generated by adjacency matrix of a graph and their sum
Asha B. Ganagia, Harishchandra S. Ramaneb a Department of Mathematics, Gogte Institute of Technology, Udyambag, Belgaum - 590008, India
b Department of Mathematics, Karnatak University, Dharwad - 580003, India
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 $\mathbb{Z}_2^n$ 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.
Received: 15.08.2013 Revised: 20.08.2014
Citation:
Asha B. Ganagi, Harishchandra S. Ramane, “Hamming distance between the strings generated by adjacency matrix of a graph and their sum”, Algebra Discrete Math., 22:1 (2016), 82–93
Linking options:
https://www.mathnet.ru/eng/adm575 https://www.mathnet.ru/eng/adm/v22/i1/p82
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Abstract page: | 200 | Full-text PDF : | 188 | References: | 24 |
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