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http://dx.doi.org/10.11568/kjm.2019.27.3.563

ON STRONG METRIC DIMENSION OF ZERO-DIVISOR GRAPHS OF RINGS  

Bhat, M. Imran (Department of Mathematics University of Kashmir)
Pirzada, Shariefuddin (Department of Mathematics University of Kashmir)
Publication Information
Korean Journal of Mathematics / v.27, no.3, 2019 , pp. 563-580 More about this Journal
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;
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