A Variant of Hop Domination in Graphs

Authors

  • Sergio Canoy, Jr. MSU-Iligan Institute of Technology, 9200 Iligan City, Philippines
  • Gemma Puebla Salasalan Mindanao State University - Iligan Institute of Technology

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i2.4352

Keywords:

hop domination, super hop domination, complement-super domination, join, lexicographic product

Keywords:

hop domination, super hop domination, complement-super domination, join, lexicographic product

Abstract

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) ∅ for
each 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.

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How to Cite

Canoy, Jr., S. ., & Salasalan, G. P. (2022). A Variant of Hop Domination in Graphs. European Journal of Pure and Applied Mathematics, 15(2), 342–353. https://doi.org/10.29020/nybg.ejpam.v15i2.4352