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

M. Imran Bhat, Shariefuddin Pirzada

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.

Keywords


Metric dimension, zero-divisor graph, strong metric dimension.

Subject classification

13A99, 05C78, 05C12.

Sponsor(s)

UGC-New Delhi

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