On the genus of graphs from commutative rings
Let be a commutative ring with non-zero identity. The cozero-divisor graph of , denoted by , is a graph with vertex-set , which is the set of all non-zero non-unit elements of , and two distinct vertices and in are adjacent if and only if and , where for , is the ideal generated by . In this paper,...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2017-04-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1016/j.akcej.2016.11.006 |
| Summary: | Let be a commutative ring with non-zero identity. The cozero-divisor graph of , denoted by , is a graph with vertex-set , which is the set of all non-zero non-unit elements of , and two distinct vertices and in are adjacent if and only if and , where for , is the ideal generated by . In this paper, we determine all isomorphism classes of finite commutative rings with identity whose has genus one. Also we characterize all non-local rings for which the reduced cozero-divisor graph is planar. |
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| ISSN: | 0972-8600 |