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Algebra and Discrete Mathematics, 2016, Volume 22, Issue 1, Pages 82–93 (Mi adm575)  

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
References:
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
Bibliographic databases:
Document Type: Article
MSC: 05C99
Language: English
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
Citation in format AMSBIB
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\by Asha~B.~Ganagi, Harishchandra~S.~Ramane
\paper Hamming distance between the strings generated by adjacency matrix of a graph and their sum
\jour Algebra Discrete Math.
\yr 2016
\vol 22
\issue 1
\pages 82--93
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3573545}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000392708800005}
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