# Some results on a supergraph of the comaximal ideal graph of a commutative ring

Document Type : Original paper

Authors

1 Saurashtra University

2 Department of Mathematics, Saurashtra University, Rajkot, Gujarat, India.

Abstract

Let $R$ be a commutative ring with identity such that $R$ admits at least two maximal ideals. In this article, we associate a graph with $R$ whose vertex set is the set of all proper ideals $I$ of $R$ such that $I$ is not contained in the Jacobson radical of $R$ and distinct vertices $I$ and $J$ are joined by an edge if and only if $I$ and $J$ are not comparable under the inclusion relation. The aim of this article is to study the interplay between the graph-theoretic properties of this graph and the ring-theoretic properties of the ring $R$.

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Main Subjects

#### References

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