DOMINATION PARAMETERS AND STRUCTURAL
PROPERTIES OF EXACT ANNIHILATING-IDEAL GRAPHS
Premkumar T. Lalchandani1, Nirali Gory2
1,2Department of Mathematics,
Dr. Subhash University,
Junagadh, 362001, India
Abstract. For a commutative ring R with identity, an ideal I is called an exact annihilating ideal if there exists a nonzero ideal J of R such that Ann(I) = J and Ann(J) = I. The exact annihilating-ideal graph EAG(R) is the simple undirected graph whose vertices are all nonzero exact annihilating ideals of R, and two distinct vertices I, J are adjacent precisely when (I, J) is an exact annihilating pair.
In this paper we develop a complete theory of domination and total domination in EAG(R). We establish, using new structural arguments and self-contained proofs, that every connected component of EAG(R) is a complete graph of order at most 2. This yields explicit formulas for the domination number γ(EAG(R)) and the total domination number γt(EAG(R)) for broad classes of rings, in-cluding reduced rings, special principal ideal rings, Artinian rings, and products of fields. Our results provide the first systematic investigation of domination parameters in exact annihilating-ideal graphs.
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to cite this paper?
DOI: 10.12732/ijam.v38i4.9
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2025
Volume: 38
Issue: 4
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