Open AccessA Variant of Hop Domination in Graphs
Author(s) -
Sergio R. Canoy,
Gemma Puebla Salasalan
Publication year - 2022
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.v15i2.4352
Subject(s) - dominating set , mathematics , combinatorics , lexicographical order , domination analysis , vertex (graph theory) , hop (telecommunications) , discrete mathematics , graph , maximal independent set , chordal graph , 1 planar graph , computer science , computer network
Let G be a connected graph with vertex and edge sets V (G) and E(G), respectively. 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. A set S ⊆ V (G) is a super hop dominating set if ehpnG(v, V (G) \ S) ≠ ∅ foreach v ∈ V (G) \ S, where ehpnG(v, V (G) \ S) is the set containing all the external hop private neighbors of v with respect to V (G) \ S. The minimum cardinality of a super hop dominating set of G, denoted by γsh(G), is called the super hop domination number of G. In this paper, we investigate the concept and study it for graphs resulting from some binary operations. Specifically, we characterize the super hop dominating sets in the join, and lexicographic products of graphs, and determine bounds of the super hop domination number of each of these graphs.