Hamming distance between the strings generated by adjacency matrix of a graph and their sum
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 \({\Bbb Z}_2^n\) of all \(n\)-tuples over the field of order two. The Hamming distance between the strings \(s(u)\) and \(s(...
Збережено в:
| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2016
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/295 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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 \({\Bbb Z}_2^n\) 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. |
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