1. Subgraph of generalized co-maximal graph of commutative rings.
- Author
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Biswas, B., Kar, S., and Sen, M. K.
- Subjects
- *
COMMUTATIVE rings , *LOCAL rings (Algebra) , *CHARTS, diagrams, etc. , *EULERIAN graphs , *GRAPH connectivity , *MATHEMATICS - Abstract
Let R be a commutative ring with 1. In Biswas et al. (Disc Math Algorithms Appl 11(1):1950013, 2019), we introduced a graph G(R) whose vertices are elements of R and two distinct vertices a, b are adjacent if and only if a R + b R = e R for some nonzero 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. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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