期刊名称：AKCE International Journal of Graphs and Combinatorics
印刷版ISSN：0972-8600
出版年度：2018
卷号：15
期号：3
页码：229-237
DOI：10.1016/j.akcej.2017.11.006
语种：English
出版社：Elsevier
摘要：AbstractLetRbe a commutative ring with identity. The nilpotent graph ofR, denoted byΓN(R), is a graph with vertex setZN(R)∗, and two verticesxandyare adjacent if and only ifxyis nilpotent, whereZN(R)={x∈R:xyis nilpotent, for somey∈R∗}. In this paper, we characterize finite rings (up to isomorphism) with identity whose nilpotent graphs can be embedded in the projective plane or Klein bottle. Also, we classify finite rings whose nilpotent graphs are ring graph or outerplanarity index 1,2.
