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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| Date: | 2016 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2016
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/155196 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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). |
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