2026-04-13T13:13:23Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/282542025-07-17T06:51:53Zcom_2072_1033col_2072_452950

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. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions Àrees temàtiques de la UPC::Matemàtiques i estadística Domination (Graph theory) Domination global domination locating domination complement graph block-cactus. Dominació (Grafs, Teoria de) 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. Postprint (published version) 2015-05-29 Article Hernando, M.; Mora, M.; Pelayo, I. M. On global location-domination in graphs. "ARS Mathematica Contemporanea", 29 Maig 2015, vol. 8, núm. 2, p. 365-379. 1855-3966 https://hdl.handle.net/2117/28254 eng http://amc-journal.eu/index.php/amc/article/view/591/799 http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Open Access Attribution-NonCommercial-NoDerivs 3.0 Spain 15 p. application/pdf