Ideal based graph structures for commutative rings

Abstract

We introduce a graph structure $\gamrr$ for commutative rings with unity. We study some of the properties of the graph $\gamrr$. Also we study some parameters of $\gamrr$ and find rings for which $\gamrr$ is split.

Keywords

• maximal ideal
• idempotent
• clique number
• domination number
• split graph