期刊名称：AKCE International Journal of Graphs and Combinatorics
印刷版ISSN：0972-8600
出版年度：2015
卷号：12
期号：2-3
页码：169-176
DOI：10.1016/j.akcej.2015.11.011
语种：English
出版社：Elsevier
摘要：AbstractLetRbe a commutative ring with identity and letZ(R,k)be the set of allk-zero-divisors inRandk>2an integer. Thek-zero-divisor hypergraphofR, denoted byHk(R), is a hypergraph with vertex setZ(R,k), and for distinct elementx1,x2,…,xkinZ(R,k), the set{x1,x2,…,xk}is an edge ofHk(R)if and only ifx1x2⋯xk=0and 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 ringsRfor which thek-zero-divisor hypergraph is planar.
