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Some Properties of the Nil-Graphs of Ideals of Commutative Rings
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| Reza Nikandish |
| , r.nikandish@ipm.ir |
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Abstract: (140 Views) |
Let R be a commutative ring with identity and Nil(R) be the set of nilpotent elements of R. The nil-graph of ideals of R is defined as the graph AG_N(R) whose vertex set is {I:(0)and there exists a non-trivial ideal  such that  and two distinct vertices  and are adjacent if and only if  . Here, we study conditions under which  is complete or bipartite. Also, the independence number of is determined, where  is a reduced ring. Finally, we classify Artinian rings whose nil-graphs of ideals have genus at most one. |
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| Keywords: Nil-graph, Complete graph, Bipartite graph, Genus, Independence number |
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Full-Text [PDF 1261 kb]
(50 Downloads)
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Type of Study: Original Manuscript |
Subject:
alg
Received: 2020/03/24 | Revised: 2023/01/22 | Accepted: 2020/12/22 | Published: 2022/12/31 | ePublished: 2022/12/31
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