RT Journal Article
T1 Domination on hyperbolic graphs
A1 Reyes Guillermo, Rosalío
A1 Rodríguez García, José Manuel
A1 Sigarreta Almira, José María
A1 Villeta, María
AB If k ≥ 1 and G = (V, E) is a finite connected graph, S ⊆ V is said a distance k-dominating set if every vertex v ∈ V is within distance k from some vertex of S. The distance k-domination number γ kw (G) is the minimum cardinality among all distance k-dominating sets of G. A set S ⊆ V is a total dominating set if every vertex v ∈ V satisfies δS (v) ≥ 1 and the total domination number, denoted by γt(G), is the minimum cardinality among all total dominating sets of G. The study of hyperbolic graphs is an interesting topic since the hyperbolicity of any geodesic metric space is equivalent to the hyperbolicity of a graph related to it. In this paper we obtain relationships between the hyperbolicity constant δ(G) and some domination parameters of a graph G. The results in this work are inequalities, such as γkw(G) ≥ 2δ(G)/(2k + 1) and δ(G) ≤ γt(G)/2 + 3.
PB Elsevier
SN 0012-365X
YR 2020
FD 2020-11
LK https://hdl.handle.net/10016/38285
UL https://hdl.handle.net/10016/38285
LA eng
NO Supported by two grants from Ministerio de Economía y Competitividad, Agencia Estatal de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) (MTM2016-78227-C2-1-P and MTM2017-90584-REDT), Spain, and a grant from Agencia Estatal de Investigación (PID2019-106433GB-I00 / AEI / 10.13039/501100011033), Spain.
DS e-Archivo
RD 17 jul. 2024