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ON THE STRONG METRIC DIMENSION OF A TOTAL GRAPH OF NONZERO ANNIHILATING IDEALS
Published online by Cambridge University Press: 04 November 2021
Abstract
Let R be a commutative ring with identity which is not an integral domain. An ideal I of R is called an annihilating ideal if there exists $r\in R- \{0\}$ such that $Ir=(0)$ . The total graph of nonzero annihilating ideals of R is the graph $\Omega (R)$ whose vertices are the nonzero annihilating ideals of R and two distinct vertices $I,J$ are joined if and only if $I+J$ is also an annihilating ideal of R. We study the strong metric dimension of $\Omega (R)$ and evaluate it in several cases.
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- Research Article
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- © The Author(s), 2021. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
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