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On the dominating sets of the complement of the annihilating ideal graph of a commutative ring
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Let R be a commutative ring with identity which is not an integral domain. Let A(R)∗ denote the collection of all nonzero annihilating ideals of R and AG(R) denote the annihilating ideal graph of R. In this article, we consider the dominating sets of (AG(R))c (where (AG(R))c is the complement of AG(R)) and study the influence of the dominating sets of (AG(R))c on the ring structure of R and vice-versa.
Title: On the dominating sets of the complement of the annihilating ideal graph of a commutative ring
Description:
Let R be a commutative ring with identity which is not an integral domain.
Let A(R)∗ denote the collection of all nonzero annihilating ideals of R and AG(R) denote the annihilating ideal graph of R.
In this article, we consider the dominating sets of (AG(R))c (where (AG(R))c is the complement of AG(R)) and study the influence of the dominating sets of (AG(R))c on the ring structure of R and vice-versa.
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Abstract
A set of vertices in a graph is a dominating set if every vertex not in the set is adjacent to at least one vertex in the set. A dominating structure is a s...