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Algebra and Discrete Mathematics, 2016, том 21, выпуск 1, страницы 128–143
(Mi adm557)
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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
RESEARCH ARTICLE
Co-intersection graph of submodules of a module
Lotf Ali Mahdavi, Yahya Talebi Department of Mathematics, Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, Iran
Аннотация:
Let $M$ be a unitary left $R$-module where $R$ is a ring with identity. The co-intersection graph of proper submodules of $M$, denoted by $\Omega(M)$, is an undirected simple graph whose the vertex set $V(\Omega)$ is a set of all non-trivial submodules of $M$ and there is an edge between two distinct vertices $N$ and $K$ if and only if $N+K\neq M$. In this paper we investigate connections between the graph-theoretic properties of $\Omega(M)$ and some algebraic properties of modules . We characterize all of modules for which the co-intersection graph of submodules is connected. Also the diameter and the girth of $\Omega(M)$ are determined. We study the clique number and the chromatic number of $\Omega(M)$.
Ключевые слова:
co-intersection graph, clique number, chromatic number.
Поступила в редакцию: 21.10.2013 Исправленный вариант: 12.09.2015
Образец цитирования:
Lotf Ali Mahdavi, Yahya Talebi, “Co-intersection graph of submodules of a module”, Algebra Discrete Math., 21:1 (2016), 128–143
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm557 https://www.mathnet.ru/rus/adm/v21/i1/p128
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Страница аннотации: | 289 | PDF полного текста: | 149 | Список литературы: | 42 |
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