Open AccessRevisiting Domination, Hop Domination, and Global Hop Domination in Graphs
Author(s) -
Gemma Puebla Salasalan,
Sergio R. Canoy
Publication year - 2021
Publication title -
european journal of pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.245
H-Index - 5
ISSN - 1307-5543
DOI - 10.29020/nybg.ejpam.v14i4.4144
Subject(s) - dominating set , mathematics , domination analysis , hop (telecommunications) , combinatorics , discrete mathematics , graph , computer science , computer network , vertex (graph theory)
A set S ⊆ V (G) is a hop dominating set of G if for each v ∈ V (G) \ S, there exists w ∈ S such that dG(v, w) = 2. It is a global hop dominating set of G if it is a hop dominating set of both G and the complement of G. The minimum cardinality of a hop dominating (global hop dominating) set of G, denoted by γh(G)(resp.γgh(G)), is called the hop domination (resp. global hop domination) number of G. In this paper, we give some realization results involving domination, hop domination, and global hop domination parameters. Also, we give a rectification of a result found in a recent paper of the authors and use this to prove some results in this paper. Â