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Closed formulae for the strong metric dimension of lexicographic product graphs

  • Identification data

    Identifier: imarina:5130478
    Authors:
    Kuziak, DorotaYero, Ismael GRodriguez-Velazquez, Juan A
    Abstract:
    Given a connected graph G, 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 metric generator for G if every pair of vertices of G is strongly resolved by some vertex of S. The smallest cardinality of a strong metric generator for G is called the strong metric dimension of G. In this paper we obtain several relationships between the strong metric dimension of the lexicographic product of graphs and the strong metric dimension of its factor graphs. © 2016, University of Zielona Gora.
  • Others:

    Author, as appears in the article.: Kuziak, Dorota; Yero, Ismael G; Rodriguez-Velazquez, Juan A
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: Rodríguez Velázquez, Juan Alberto
    Keywords: Strong metric generator Strong metric dimension Strong metric basis Lexicographic product graphs
    Abstract: Given a connected graph G, 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 metric generator for G if every pair of vertices of G is strongly resolved by some vertex of S. The smallest cardinality of a strong metric generator for G is called the strong metric dimension of G. In this paper we obtain several relationships between the strong metric dimension of the lexicographic product of graphs and the strong metric dimension of its factor graphs. © 2016, University of Zielona Gora.
    Thematic Areas: Mathematics Matemática / probabilidade e estatística Discrete mathematics and combinatorics Ciência da computação Applied mathematics
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Author's mail: juanalberto.rodriguez@urv.cat
    Author identifier: 0000-0002-9082-7647
    Record's date: 2024-10-26
    Papper version: info:eu-repo/semantics/publishedVersion
    Link to the original source: https://www.dmgt.uz.zgora.pl/publish/volume.php?volume=36_4
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Papper original source: Discussiones Mathematicae Graph Theory. 36 (4): 1051-1064
    APA: Kuziak, Dorota; Yero, Ismael G; Rodriguez-Velazquez, Juan A (2016). Closed formulae for the strong metric dimension of lexicographic product graphs. Discussiones Mathematicae Graph Theory, 36(4), 1051-1064. DOI: 10.7151/dmgt.1911
    Article's DOI: 10.7151/dmgt.1911
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2016
    Publication Type: Journal Publications
  • Keywords:

    Applied Mathematics,Discrete Mathematics and Combinatorics,Mathematics
    Strong metric generator
    Strong metric dimension
    Strong metric basis
    Lexicographic product graphs
    Mathematics
    Matemática / probabilidade e estatística
    Discrete mathematics and combinatorics
    Ciência da computação
    Applied mathematics
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