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,...
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Taylor & Francis Group
2017-04-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
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| Online Access: | http://dx.doi.org/10.1016/j.akcej.2016.11.006 |
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doaj-617fa86739b6430bbc63aaf9eb72167a2020-11-25T03:35:35ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002017-04-01141273410.1016/j.akcej.2016.11.00612092611On the genus of graphs from commutative ringsS. Kavitha0R. Kala1Department of Mathematics, Manonmaniam Sundaranar UniversityDepartment of Mathematics, Manonmaniam Sundaranar UniversityLet 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.http://dx.doi.org/10.1016/j.akcej.2016.11.006genuslocal ringnilpotentplanar graph |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
S. Kavitha R. Kala |
| spellingShingle |
S. Kavitha R. Kala On the genus of graphs from commutative rings AKCE International Journal of Graphs and Combinatorics genus local ring nilpotent planar graph |
| author_facet |
S. Kavitha R. Kala |
| author_sort |
S. Kavitha |
| title |
On the genus of graphs from commutative rings |
| title_short |
On the genus of graphs from commutative rings |
| title_full |
On the genus of graphs from commutative rings |
| title_fullStr |
On the genus of graphs from commutative rings |
| title_full_unstemmed |
On the genus of graphs from commutative rings |
| title_sort |
on the genus of graphs from commutative rings |
| publisher |
Taylor & Francis Group |
| series |
AKCE International Journal of Graphs and Combinatorics |
| issn |
0972-8600 |
| publishDate |
2017-04-01 |
| description |
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. |
| topic |
genus local ring nilpotent planar graph |
| url |
http://dx.doi.org/10.1016/j.akcej.2016.11.006 |
| work_keys_str_mv |
AT skavitha onthegenusofgraphsfromcommutativerings AT rkala onthegenusofgraphsfromcommutativerings |
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1724553621090074624 |