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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access October 9, 2014

On the strong metric dimension of the strong products of graphs

  • Dorota Kuziak , Ismael G. Yero EMAIL logo and Juan A. Rodríguez-Velázquez EMAIL logo
From the journal Open Mathematics


Let G be a connected graph. A vertex w ∈ V.G/ strongly resolves two vertices u,v ∈ V.G/ if there exists some shortest u-w path containing v or some shortest v-w path containing u. A set S of vertices is a strong resolving set for G if every pair of vertices of G is strongly resolved by some vertex of S. The smallest cardinality of a strong resolving set for G is called the strong metric dimension of G. It is well known that the problem of computing this invariant is NP-hard. In this paper we study the problem of finding exact values or sharp bounds for the strong metric dimension of strong product graphs and express these in terms of invariants of the factor graphs.


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Received: 2013-8-28
Accepted: 2014-7-11
Published Online: 2014-10-9
Published in Print: 2015-1-1

© 2015 Dorota Kuziak et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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