On the planarity of the k-zero-divisor hypergraphs
Let R be a commutative ring with identity and let Z(R,k) be the set of all k-zero-divisors in R and k>2 an integer. The k-zero-divisor hypergraph of R, denoted by Hk(R), is a hypergraph with vertex set Z(R,k), and for distinct element x1,x2,…,xk in Z(R,k), the set {x1,x2,…,xk} is an edge of Hk(R)...
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Taylor & Francis Group
2015-11-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S0972860015000389 |
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doaj-328e73e1ee0042dfabf671454a86731f2020-11-25T03:24:41ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002015-11-0112216917610.1016/j.akcej.2015.11.011On the planarity of the k-zero-divisor hypergraphsT. Tamizh ChelvamK. SelvakumarV. RamanathanLet R be a commutative ring with identity and let Z(R,k) be the set of all k-zero-divisors in R and k>2 an integer. The k-zero-divisor hypergraph of R, denoted by Hk(R), is a hypergraph with vertex set Z(R,k), and for distinct element x1,x2,…,xk in Z(R,k), the set {x1,x2,…,xk} is an edge of Hk(R) if and only if x1x2⋯xk=0 and the product of elements of no (k−1)-subset of {x1,x2,…,xk} is zero. In this paper, we characterize all finite commutative non-local rings R for which the k-zero-divisor hypergraph is planar.http://www.sciencedirect.com/science/article/pii/S0972860015000389HypergraphZero-divisor graphPlanar hypergraphIncidence graph |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
T. Tamizh Chelvam K. Selvakumar V. Ramanathan |
| spellingShingle |
T. Tamizh Chelvam K. Selvakumar V. Ramanathan On the planarity of the k-zero-divisor hypergraphs AKCE International Journal of Graphs and Combinatorics Hypergraph Zero-divisor graph Planar hypergraph Incidence graph |
| author_facet |
T. Tamizh Chelvam K. Selvakumar V. Ramanathan |
| author_sort |
T. Tamizh Chelvam |
| title |
On the planarity of the k-zero-divisor hypergraphs |
| title_short |
On the planarity of the k-zero-divisor hypergraphs |
| title_full |
On the planarity of the k-zero-divisor hypergraphs |
| title_fullStr |
On the planarity of the k-zero-divisor hypergraphs |
| title_full_unstemmed |
On the planarity of the k-zero-divisor hypergraphs |
| title_sort |
on the planarity of the k-zero-divisor hypergraphs |
| publisher |
Taylor & Francis Group |
| series |
AKCE International Journal of Graphs and Combinatorics |
| issn |
0972-8600 |
| publishDate |
2015-11-01 |
| description |
Let R be a commutative ring with identity and let Z(R,k) be the set of all k-zero-divisors in R and k>2 an integer. The k-zero-divisor hypergraph of R, denoted by Hk(R), is a hypergraph with vertex set Z(R,k), and for distinct element x1,x2,…,xk in Z(R,k), the set {x1,x2,…,xk} is an edge of Hk(R) if and only if x1x2⋯xk=0 and the product of elements of no (k−1)-subset of {x1,x2,…,xk} is zero. In this paper, we characterize all finite commutative non-local rings R for which the k-zero-divisor hypergraph is planar. |
| topic |
Hypergraph Zero-divisor graph Planar hypergraph Incidence graph |
| url |
http://www.sciencedirect.com/science/article/pii/S0972860015000389 |
| work_keys_str_mv |
AT ttamizhchelvam ontheplanarityofthekzerodivisorhypergraphs AT kselvakumar ontheplanarityofthekzerodivisorhypergraphs AT vramanathan ontheplanarityofthekzerodivisorhypergraphs |
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1724600594119786496 |