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Resolvability and Strong Resolvability in the Direct Product of Graphs

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Abstract

Given a connected graph G, a vertex \({w \in V(G)}\) distinguishes two different vertices u, v of G if the distances between w and u, and between w and v are different. Moreover, w strongly resolves the pair u, v if there exists some shortest u−w path containing v or some shortest v−w path containing u. A set W of vertices is a (strong) metric generator for G if every pair of vertices of G is (strongly resolved) distinguished by some vertex of W. The smallest cardinality of a (strong) metric generator for G is called the (strong) metric dimension of G. In this article we study the (strong) metric dimension of some families of direct product graphs.

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Authors and Affiliations

  1. Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Av. Països Catalans 26, 43007, Tarragona, Spain

    Dorota Kuziak

  2. University of Maribor, FEECS, Smetanova 17, 2000, Maribor, Slovenia

    Iztok Peterin

  3. IMFM, Jadranska 19, 1000, Ljubljana, Slovenia

    Iztok Peterin

  4. Departamento de Matemáticas EPS, Universidad de Cádiz, Av. Ramón Puyol s/n, 11202, Algeciras, Spain

    Ismael G. Yero

Authors
  1. Dorota Kuziak
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  2. Iztok Peterin
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  3. Ismael G. Yero
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Correspondence to Ismael G. Yero.

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Kuziak, D., Peterin, I. & Yero, I.G. Resolvability and Strong Resolvability in the Direct Product of Graphs. Results Math 71, 509–526 (2017). https://doi.org/10.1007/s00025-016-0563-6

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  • DOI: https://doi.org/10.1007/s00025-016-0563-6

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