Articles producció científica> Enginyeria Informàtica i Matemàtiques

WEAK TOTAL RESOLVABILITY IN GRAPHS

  • Datos identificativos

    Identificador: imarina:9295799
    Autores:
    Casel, KatrinEstrada-Moreno, AlejandroFernau, HenningAlberto Rodriguez-Velazquez, Juan
    Resumen:
    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.
  • Otros:

    Autor según el artículo: Casel, Katrin; Estrada-Moreno, Alejandro; Fernau, Henning; Alberto Rodriguez-Velazquez, Juan
    Departamento: Enginyeria Informàtica i Matemàtiques
    Autor/es de la URV: Estrada Moreno, Alejandro / Rodríguez Velázquez, Juan Alberto
    Palabras clave: Weak total resolving set Weak total metric dimension Resolving set Metric dimension Graph operations Adjacency dimension
    Resumen: 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.
    Áreas temáticas: Mathematics Matemática / probabilidade e estatística Discrete mathematics and combinatorics Ciência da computação Applied mathematics
    Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
    Direcció de correo del autor: alejandro.estrada@urv.cat juanalberto.rodriguez@urv.cat
    Identificador del autor: 0000-0001-9767-2177 0000-0002-9082-7647
    Fecha de alta del registro: 2024-10-26
    Versión del articulo depositado: info:eu-repo/semantics/publishedVersion
    Enlace a la fuente original: https://www.dmgt.uz.zgora.pl/publish/volume.php?volume=36_1
    URL Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
    Referencia al articulo segun fuente origial: Discussiones Mathematicae Graph Theory. 36 (1): 185-210
    Referencia 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 del artículo: 10.7151/dmgt.1853
    Entidad: Universitat Rovira i Virgili
    Año de publicación de la revista: 2016
    Tipo de publicación: Journal Publications
  • Palabras clave:

    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
  • Documentos:

  • Cerca a google

    Search to google scholar