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: 2023-04-29
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
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
URL Document de llicència: http://repositori.urv.cat/ca/proteccio-de-dades/
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
Repositori URV