Co-intersection graph of submodules of a module
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 betwe...
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| Дата: | 2016 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2016
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-1072016-05-11T05:58:15Z Co-intersection graph of submodules of a module Mahdavi, Lotf Ali Talebi, Yahya co-intersection graph, clique number, chromatic number 05C15, 05C25, 05C69, 16D10 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 \(\Omega(M)\). Lugansk National Taras Shevchenko University 2016-05-10 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/107 Algebra and Discrete Mathematics; Vol 21, No 1 (2016) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/107/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/107/19 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/107/20 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/107/21 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/107/22 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/107/23 Copyright (c) 2016 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
co-intersection graph clique number chromatic number 05C15 05C25 05C69 16D10 |
| spellingShingle |
co-intersection graph clique number chromatic number 05C15 05C25 05C69 16D10 Mahdavi, Lotf Ali Talebi, Yahya Co-intersection graph of submodules of a module |
| topic_facet |
co-intersection graph clique number chromatic number 05C15 05C25 05C69 16D10 |
| format |
Article |
| author |
Mahdavi, Lotf Ali Talebi, Yahya |
| author_facet |
Mahdavi, Lotf Ali Talebi, Yahya |
| author_sort |
Mahdavi, Lotf Ali |
| title |
Co-intersection graph of submodules of a module |
| title_short |
Co-intersection graph of submodules of a module |
| title_full |
Co-intersection graph of submodules of a module |
| title_fullStr |
Co-intersection graph of submodules of a module |
| title_full_unstemmed |
Co-intersection graph of submodules of a module |
| title_sort |
co-intersection graph of submodules of a module |
| description |
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 \(\Omega(M)\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2016 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/107 |
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AT mahdavilotfali cointersectiongraphofsubmodulesofamodule AT talebiyahya cointersectiongraphofsubmodulesofamodule |
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2024-04-12T06:27:19Z |
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2024-04-12T06:27:19Z |
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