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arXiv · 2208.08095

Computing the strong metric dimension for co-maximal ideal graphs of commutative rings

R. Shahriyari·R. Nikandish·A. Tehranian·H. Rasouli
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Abstract

Let $R$ be a commutative ring with identity. The co-maximal ideal graph of $R$, denoted by $\Gamma(R)$, is a simple graph whose vertices are proper ideals of $R$ which are not contained in the Jacobson radical of $R$ and two distinct vertices $I, J$ are adjacent if and only if $I+J=R$. In this paper, we use Gallai$^{^,}$s Theorem and the concept of strong resolving graph to compute the strong metric dimension for co-maximal ideal graphs of commutative rings. Explicit formulae for the strong metric dimension, depending on whether the ring is reduced or not, are established.

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R. Shahriyari, R. Nikandish, A. Tehranian, H. Rasouli. 2022-08-17. Computing the strong metric dimension for co-maximal ideal graphs of commutative rings. https://arxiv.org/abs/2208.08095

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