Locating-dominating sets and identifying codes in Graphs of Girth at least 5

Locating-dominating sets and identifying codes are two closely related notions in the area of separating systems. Roughly speaking, they consist in a dominating set of a graph such that every vertex is uniquely identified by its neighbourhood within the dominating set. In this paper, we study the si...

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Detalhes bibliográficos
Autores: Balbuena Martínez, Maria Camino Teófila|||0000-0003-4190-4287, Foucaud, Florent, Hansberg Pastor, Adriana
Formato: artículo
Fecha de publicación:2015
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/78501
Acesso em linha:https://hdl.handle.net/2117/78501
Access Level:acceso abierto
Palavra-chave:Graph theory
Identifying codes
locating-dominating sets
dominating sets
girth
path covers
minimum degree
COMPLEXITY
SYSTEMS
NUMBER
BOUNDS
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
Descrição
Resumo:Locating-dominating sets and identifying codes are two closely related notions in the area of separating systems. Roughly speaking, they consist in a dominating set of a graph such that every vertex is uniquely identified by its neighbourhood within the dominating set. In this paper, we study the size of a smallest locating-dominating set or identifying code for graphs of girth at least 5 and of given minimum degree. We use the technique of vertex-disjoint paths to provide upper bounds on the minimum size of such sets, and construct graphs who come close to meeting these bounds.