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WEAK TOTAL RESOLVABILITY IN GRAPHS

  • Dades identificatives

    Identificador: imarina:9295799
    Autors:
    Casel, KatrinEstrada-Moreno, AlejandroFernau, HenningAlberto Rodriguez-Velazquez, Juan
    Resum:
    A vertex v is an element of V(G) is said to distinguish two vertices x, y is an element of V(G) of a graph G if the distance from v to x is different from the distance from v to y. A set W subset of V(G) is a total resolving set for a graph G if for every pair of vertices x, y is an element of V(G), there exists some vertex w is an element of W {x, y} which distinguishes x and y, while W is a weak total resolving set if for every x is an element of V(G) W and y is an element of W, there exists some w is an element of W {y} which distinguishes x and y. A weak total resolving set of minimum cardinality is called a weak total metric basis of G and its cardinality the weak total metric dimension of G. Our main contributions are the following ones: (a) Graphs with small and large weak total metric bases are characterised. (b) We explore the (tight) relation to independent 2-domination. (c) We introduce a new graph parameter, called weak total adjacency dimension and present results that are analogous to those presented for weak total dimension. (d) For trees, we derive a characterisation of the weak total (adjacency) metric dimension. Also, exact figures for our parameters are presented for (generalised) fans and wheels. (e) We show that for Cartesian product graphs, the weak total (adjacency) metric dimension is usually pretty small. (f) The weak total (adjacency) dimension is studied for lexicographic products of graphs.
  • Altres:

    Autor segons l'article: Casel, Katrin; Estrada-Moreno, Alejandro; Fernau, Henning; Alberto Rodriguez-Velazquez, Juan
    Departament: Enginyeria Informàtica i Matemàtiques
    Autor/s de la URV: Estrada Moreno, Alejandro / Rodríguez Velázquez, Juan Alberto
    Paraules clau: Weak total resolving set Weak total metric dimension Resolving set Metric dimension Graph operations Adjacency dimension
    Resum: A vertex v is an element of V(G) is said to distinguish two vertices x, y is an element of V(G) of a graph G if the distance from v to x is different from the distance from v to y. A set W subset of V(G) is a total resolving set for a graph G if for every pair of vertices x, y is an element of V(G), there exists some vertex w is an element of W {x, y} which distinguishes x and y, while W is a weak total resolving set if for every x is an element of V(G) W and y is an element of W, there exists some w is an element of W {y} which distinguishes x and y. A weak total resolving set of minimum cardinality is called a weak total metric basis of G and its cardinality the weak total metric dimension of G. Our main contributions are the following ones: (a) Graphs with small and large weak total metric bases are characterised. (b) We explore the (tight) relation to independent 2-domination. (c) We introduce a new graph parameter, called weak total adjacency dimension and present results that are analogous to those presented for weak total dimension. (d) For trees, we derive a characterisation of the weak total (adjacency) metric dimension. Also, exact figures for our parameters are presented for (generalised) fans and wheels. (e) We show that for Cartesian product graphs, the weak total (adjacency) metric dimension is usually pretty small. (f) The weak total (adjacency) dimension is studied for lexicographic products of graphs.
    Àrees temàtiques: Mathematics Matemática / probabilidade e estatística Discrete mathematics and combinatorics Ciência da computação Applied mathematics
    Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
    Adreça de correu electrònic de l'autor: alejandro.estrada@urv.cat juanalberto.rodriguez@urv.cat
    Identificador de l'autor: 0000-0001-9767-2177 0000-0002-9082-7647
    Data d'alta del registre: 2024-10-26
    Versió de l'article dipositat: info:eu-repo/semantics/publishedVersion
    Enllaç font original: https://www.dmgt.uz.zgora.pl/publish/volume.php?volume=36_1
    URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
    Referència a l'article segons font original: Discussiones Mathematicae Graph Theory. 36 (1): 185-210
    Referència de l'ítem segons les normes APA: Casel, Katrin; Estrada-Moreno, Alejandro; Fernau, Henning; Alberto Rodriguez-Velazquez, Juan (2016). WEAK TOTAL RESOLVABILITY IN GRAPHS. Discussiones Mathematicae Graph Theory, 36(1), 185-210. DOI: 10.7151/dmgt.1853
    DOI de l'article: 10.7151/dmgt.1853
    Entitat: Universitat Rovira i Virgili
    Any de publicació de la revista: 2016
    Tipus de publicació: Journal Publications
  • Paraules clau:

    Applied Mathematics,Discrete Mathematics and Combinatorics,Mathematics
    Weak total resolving set
    Weak total metric dimension
    Resolving set
    Metric dimension
    Graph operations
    Adjacency dimension
    Mathematics
    Matemática / probabilidade e estatística
    Discrete mathematics and combinatorics
    Ciência da computação
    Applied mathematics
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