期刊名称：AKCE International Journal of Graphs and Combinatorics
印刷版ISSN：0972-8600
出版年度：2017
卷号：14
期号：1
页码：27-34
DOI：10.1016/j.akcej.2016.11.006
语种：English
出版社：Elsevier
摘要：Abstract Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R , denoted by Γ ′ ( R ) , is a graph with vertex-set W ∗ ( R ) , which is the set of all non-zero non-unit elements of R , and two distinct vertices x and y in W ∗ ( R ) are adjacent if and only if x ∉ R y and y ∉ R x , where for z ∈ R , R z is the ideal generated by z . In this paper, we determine all isomorphism classes of finite commutative rings R with identity whose Γ ′ ( R ) has genus one. Also we characterize all non-local rings for which the reduced cozero-divisor graph Γ r ( R ) is planar.
