The Local Metric Dimension of Strong Product Graphs |
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Authors: | Gabriel A Barragán-Ramírez Juan A Rodríguez-Velázquez |
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Institution: | 1.Departament d’Enginyeria Informàtica i Matemàtiques,Universitat Rovira i Virgili,Tarragona,Spain |
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Abstract: | A vertex \(v\in V(G)\) is said to distinguish two vertices \(x,y\in V(G)\) of a nontrivial connected graph G if the distance from v to x is different from the distance from v to y. A set \(S\subset V(G)\) is a local metric generator for G if every two adjacent vertices of G are distinguished by some vertex of S. A local metric generator with the minimum cardinality is called a local metric basis for G and its cardinality, the local metric dimension of G. It is known that the problem of computing the local metric dimension of a graph is NP-Complete. In this paper we study the problem of finding exact values or bounds for the local metric dimension of strong product of graphs. |
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