A graph associated with minimal ideals of a ring

Document Type : Research Paper

Authors

1 Department of Mathematics, Cotton University, India

2 Department of Mathematics Cotton University, India

Abstract

‎In this paper‎, ‎a new kind of graph is introduced and investigated‎. ‎The minimal ideal graph for a ring $R$ with unity is an undirected graph whose vertex set contains all non-trivial ideals of $R$‎. ‎We denote the graph by $mI(R)$ and the vertex set by $V(mI(R))$‎. ‎Two vertices $P,Q \in V(mI(R))$ are adjacent if a minimal ideal $p$ of $R$ exists with $p\subset P$ and $p \subset Q$‎. ‎We study the correlation of algebraic properties and graph theoretic properties of $mI(R)$‎. ‎In this article‎, ‎connectedness‎, ‎diameter‎, ‎clique number‎, ‎chromatic number‎, ‎regular character‎, ‎cut vertex etc‎. ‎are discussed‎.

Keywords

References

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Journal of Algebra and Related Topics
Volume 12, Issue 2
January 2025
Pages 155-163

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