A note on zero-divisor graph of amalgamated duplication of a ring along an ideal

Abstract

Let be a commutative ring and be a non-zero ideal of . Let be the subring of consisting of the elements for and . In this paper we characterize all isomorphism classes of finite commutative rings with identity and ideal such that is planar. We determine the number of vertices of , a necessary and sufficient condition for the graph to be outerplanar and the domination number of .

Keywords

• planar
• outerplanar
• complete graph
• genus
• domination