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 Ω(M), is an undirected simple graph whose the vertex set V(Ω) is a set of all non-trivial submodules of M and there is an edge between two distinct vertices N and K if an...
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| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2016
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/155196 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Co-intersection graph of submodules of a module / L.A. Mahdavi, Y. Talebi // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 1. — С. 128-143. — Бібліогр.: 11 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-155196 |
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irk-123456789-1551962019-06-17T01:26:09Z Co-intersection graph of submodules of a module Mahdavi, L.A. Talebi, Y. 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 Ω(M), is an undirected simple graph whose the vertex set V(Ω) 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≠M. In this paper we investigate connections between the graph-theoretic properties of Ω(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 Ω(M) are determined. We study the clique number and the chromatic number of Ω(M). 2016 Article Co-intersection graph of submodules of a module / L.A. Mahdavi, Y. Talebi // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 1. — С. 128-143. — Бібліогр.: 11 назв. — англ. 1726-3255 2010 MSC:05C15, 05C25, 05C69, 16D10. http://dspace.nbuv.gov.ua/handle/123456789/155196 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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 Ω(M), is an undirected simple graph whose the vertex set V(Ω) 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≠M. In this paper we investigate connections between the graph-theoretic properties of Ω(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 Ω(M) are determined. We study the clique number and the chromatic number of Ω(M). |
| format |
Article |
| author |
Mahdavi, L.A. Talebi, Y. |
| spellingShingle |
Mahdavi, L.A. Talebi, Y. Co-intersection graph of submodules of a module Algebra and Discrete Mathematics |
| author_facet |
Mahdavi, L.A. Talebi, Y. |
| author_sort |
Mahdavi, L.A. |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/155196 |
| citation_txt |
Co-intersection graph of submodules of a module / L.A. Mahdavi, Y. Talebi // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 1. — С. 128-143. — Бібліогр.: 11 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT mahdavila cointersectiongraphofsubmodulesofamodule AT talebiy cointersectiongraphofsubmodulesofamodule |
| first_indexed |
2023-05-20T17:46:18Z |
| last_indexed |
2023-05-20T17:46:18Z |
| _version_ |
1796154051876880384 |