Subgraph of generalized co-maximal graph of commutative rings
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Abstract Let R be a commutative ring with 1. In [3], we introduced a graph G(R) whose vertices are elements of R and two distinct vertices a, b are adjacent if and only if aR + bR = eR for some non-zero idempotent e in R. Let G′(R) be the subgraph of G(R) generated by the non-units of R. In this paper, we characterize those rings R for which the graph G′(R) is connected and Eulerian. Also we characterize those rings R for which genus of the graph G′(R) is ≤ 2. Finally, we show that the graph G′(R) is a line graph of some graph if and only if R is either a regular ring or a local ring.AMS Subject Classification 2020 : 05C25
2019 ◽
Vol 19
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pp. 2050173
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2014 ◽
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2013 ◽
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2011 ◽
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pp. 665-674
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2007 ◽
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pp. 527-555
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2012 ◽
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