Locating domination in bipartite graphs and their complements

A set S of vertices of a graph G is distinguishing if the sets of neighbors in S for every pair of vertices not in S are distinct. A locating-dominating set of G is a dominating distinguishing set. The location-domination number of G , ¿ ( G ), is the minimum cardinality of a locating-dominating set...

Descripción completa

Detalles Bibliográficos
Autores: Hernando Martín, María del Carmen|||0000-0002-3864-6566, Mora Giné, Mercè|||0000-0001-6923-0320, Pelayo Melero, Ignacio Manuel|||0000-0002-6523-0611
Tipo de recurso: informe técnico
Fecha de publicación:2017
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/111067
Acceso en línea:https://hdl.handle.net/2117/111067
Access Level:acceso abierto
Palabra clave:Graph theory
domination
location
distinguishing set
locating domination
complement graph
bipartite graph
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística
Descripción
Sumario:A set S of vertices of a graph G is distinguishing if the sets of neighbors in S for every pair of vertices not in S are distinct. A locating-dominating set of G is a dominating distinguishing set. The location-domination number of G , ¿ ( G ), is the minimum cardinality of a locating-dominating set. In this work we study relationships between ¿ ( G ) and ¿ ( G ) for bipartite graphs. The main result is the characterization of all connected bipartite graphs G satisfying ¿ ( G ) = ¿ ( G ) + 1. To this aim, we define an edge-labeled graph G S associated with a distinguishing set S that turns out to be very helpful