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On global location-domination in graphs
Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta; Universitat Politècnica de Catalunya. COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions
A dominating set S of a graph G is called locating-dominating, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locating-dominating sets of minimum cardinality are called LD-codes and the cardinality of an LD-code is the location-domination number lambda(G). An LD-set S of a graph G is global if it is an LD-set of both G and its complement G'. The global location-domination number lambda g(G) is introduced as the minimum cardinality of a global LD-set of G. In this paper, some general relations between LD-codes and the location-domination number in a graph and its complement are presented first. Next, a number of basic properties involving the global location-domination number are showed. Finally, both parameters are studied in-depth for the family of block-cactus graphs.
Àrees temàtiques de la UPC::Matemàtiques i estadística
Domination (Graph theory)
Domination
global domination
locating domination
complement graph
block-cactus.
Dominació (Grafs, Teoria de)
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/publishedVersion
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