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Computing the (forcing) strong metric dimension in strongly annihilating-ideal graphs

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Abstract

The strongly annihilating-ideal graph \(\textrm{SAG}(R)\) of a commutative unital ring R is a simple graph whose vertices are non-zero ideals of R with non-zero annihilator and there exists an edge between two distinct vertices if and only if each of them has a non-zero intersection with annihilator of the other one. In this paper, we compute twin-free clique number of \(\textrm{SAG}(R)\) and as an application strong metric dimension of \(\textrm{SAG}(R)\) is given. Moreover, we investigate the structures of strong resolving sets in \(\textrm{SAG}(R)\) to find forcing strong metric dimension in \(\textrm{SAG}(R)\).

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Acknowledgements

The authors express their deep gratitude to the referees for their valuable suggestions which definitely improved the paper.

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Authors and Affiliations

  1. Department of Mathematics, Parand Branch, Islamic Azad University, Parand, Iran

    M. Pazoki

  2. Department of Mathematics, Jundi-Shapur University of Technology, Dezful, P.O. BOX 64615-334, Iran

    R. Nikandish

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  1. M. Pazoki
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  2. R. Nikandish
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Correspondence to R. Nikandish.

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Pazoki, M., Nikandish, R. Computing the (forcing) strong metric dimension in strongly annihilating-ideal graphs. AAECC (2023). https://doi.org/10.1007/s00200-023-00601-x

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  • DOI: https://doi.org/10.1007/s00200-023-00601-x

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