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Computing the metric dimension of a graph from primary subgraphs

  • Identification data

    Identifier: imarina:5130633
    Authors:
    Kuziak, DorotaRodriguez-Velazquez, Juan AYero, Ismael G
    Abstract:
    Let G be a connected graph. Given an ordered set W = {w1, . . . , wk} V (G) and a vertex u V (G), the representation of u with respect to W is the ordered k-tuple (d(u, w1), d(u, w2), . . . , d(u, wk)), where d(u, wi) denotes the distance between u and wi. The set W is a metric generator for G if every two different vertices of G have distinct representations. A minimum cardinality metric generator is called a metric basis of G and its cardinality is called the metric dimension of G. It is well known that the problem of finding the metric dimension of a graph is NP-hard. In this paper we obtain closed formulae for the metric dimension of graphs with cut vertices. The main results are applied to specific constructions including rooted product graphs, corona product graphs, block graphs and chains of graphs.
  • Others:

    Author, as appears in the article.: Kuziak, Dorota; Rodriguez-Velazquez, Juan A; Yero, Ismael G
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: Rodríguez Velázquez, Juan Alberto
    Keywords: Rooted product graphs Primary subgraphs Metric dimension Metric basis Corona product graphs
    Abstract: Let G be a connected graph. Given an ordered set W = {w1, . . . , wk} V (G) and a vertex u V (G), the representation of u with respect to W is the ordered k-tuple (d(u, w1), d(u, w2), . . . , d(u, wk)), where d(u, wi) denotes the distance between u and wi. The set W is a metric generator for G if every two different vertices of G have distinct representations. A minimum cardinality metric generator is called a metric basis of G and its cardinality is called the metric dimension of G. It is well known that the problem of finding the metric dimension of a graph is NP-hard. In this paper we obtain closed formulae for the metric dimension of graphs with cut vertices. The main results are applied to specific constructions including rooted product graphs, corona product graphs, block graphs and chains of graphs.
    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=37_1
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Papper original source: Discussiones Mathematicae Graph Theory. 37 (1): 273-293
    APA: Kuziak, Dorota; Rodriguez-Velazquez, Juan A; Yero, Ismael G (2017). Computing the metric dimension of a graph from primary subgraphs. Discussiones Mathematicae Graph Theory, 37(1), 273-293. DOI: 10.7151/dmgt.1934
    Article's DOI: 10.7151/dmgt.1934
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2017
    Publication Type: Journal Publications
  • Keywords:

    Applied Mathematics,Discrete Mathematics and Combinatorics,Mathematics
    Rooted product graphs
    Primary subgraphs
    Metric dimension
    Metric basis
    Corona product graphs
    Mathematics
    Matemática / probabilidade e estatística
    Discrete mathematics and combinatorics
    Ciência da computação
    Applied mathematics
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