Korean J. Math. Vol. 27 No. 3 (2019) pp.563-580
DOI: https://doi.org/10.11568/kjm.2019.27.3.563

On strong metric dimension of zero-divisor graphs of rings

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Published: Sep 30, 2019
Keywords:
Metric dimension, zero-divisor graph, strong metric dimension.
Mathematics Subject Classification:
13A99, 05C78, 05C12.

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M. Imran Bhat
Department of Mathematics University of Kashmir Srinagar, 190006, Srinagar, Kashmir, India
Shariefuddin Pirzada
Department of Mathematics University of Kashmir Srinagar, 190006, Kashmir, India

Abstract

In this paper, we study the strong metric dimension of zero-divisor graph $\Gamma(R)$ associated to a ring $R$. This is done by transforming the problem into a more well-known problem of finding the vertex cover number $\alpha(G)$ of a strong resolving graph $G_{sr}$. We find the strong metric dimension of zero-divisor graphs of the ring $\mathbb{Z}_n$ of integers modulo $n$ and the ring of Gaussian integers $\mathbb{Z}_n[i]$ modulo $n$. We obtain the bounds for strong metric dimension of zero-divisor graphs and we also discuss the strong metric dimension of the Cartesian product of graphs.


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Supporting Agencies

UGC-New Delhi

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