Some properties of the essential annihilating-ideal graph of commutative rings

Document Type : Original paper

Authors

1 Department of mathematics, Aligarh Muslim University, Aligarh.

2 Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India

Abstract

Let S be a commutative ring with unity and A(S) denotes the set of annihilating-ideals of S. The essential annihilating-ideal graph of S, denoted by EG(S), is an undirected graph with A∗(S) as the set of vertices and   for distinct I,J∈A∗(S), I∼J is an edge if and only if Ann(IJ)≤eS. In this paper, we classify the Artinian rings S for which EG(S) is projective. We also discuss the coloring of EG(S). Moreover, we discuss the domination number of EG(S).

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References

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Communications in Combinatorics and Optimization
Volume 8, Issue 4
December 2023
Pages 715-724

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