On the planarity of the k-zero-divisor hypergraphs

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ID: 46028
2015
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Ranked #1 of 11 articles by views in akce international journal of graphs and combinatorics

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Abstract
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.
Reference Key
chelvam2015onakce Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors T. Tamizh Chelvam, K. Selvakumar, V. Ramanathan
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Journal akce international journal of graphs and combinatorics
Year 2015
DOI
DOI not found
URL
http://www.sciencedirect.com/science/article/pii/S0972860015000389
Keywords
mathematics

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