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:: Volume 8, Issue 4 (Vol. 8,No. 4, 2022) ::
2022, 8(4): 238-255 Back to browse issues page
Some Properties of the Nil-Graphs of Ideals of Commutative Rings
Reza Nikandish
, r.nikandish@ipm.ir
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.
Keywords: Nil-graph, Complete graph, Bipartite graph, Genus, Independence number
Full-Text [PDF 1261 kb]   (50 Downloads)    
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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Nikandish R. Some Properties of the Nil-Graphs of Ideals of Commutative Rings. Journal title 2022; 8 (4) :238-255
URL: http://mmr.khu.ac.ir/article-1-3071-en.html


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Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Volume 8, Issue 4 (Vol. 8,No. 4, 2022) Back to browse issues page
پژوهش‌های ریاضی Mathematical Researches
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