Title of article
Some properties of the essential annihilating-ideal graph of commutative rings
Author/Authors
Nazim ، Mohd Department of mathematics - Aligarh Muslim University , Rehman ، Nadeem ur Department of Mathematics - Aligarh Muslim University , Mir ، Shabir Ahmad Department of Mathematics - Aligarh Muslim University
From page
715
To page
724
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 ) ≤e S. 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).
Keywords
Annihilating , ideal graph , essential annihilating , ideal graph , crosscap of a graph , domination number of a graph
Journal title
Communications in Combinatorics and Optimization
Journal title
Communications in Combinatorics and Optimization
Record number
2741124
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