Hop Independent Sets in Graphs

Authors

  • Javier Hassan MSU-Iligan Institute of Technology, Philippines
  • Sergio R. Canoy, Jr. MSU-Iligan Institute of Technology, Philippines
  • Alkajim A. Aradais Mindanao State University-TCTO, Philippines

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i2.4350

Keywords:

locating, stable, domination, join, corona

Keywords:

locating, stable, domination, join, corona

Abstract

Let G be an undirected graph with vertex and edge sets V (G) and E(G), respectively. A set S ⊆ V (G) is a hop independent set of G if any two distinct vertices in S are not at a distance two from each other, that is, dG(v, w) 6= 2 for any distinct vertices v, w ∈ S. The maximum cardinality of a hop independent set of G, denoted by αh(G), is called the hop independence number of G. In this paper, we show that the absolute difference of the independence number and the hop independence number of a graph can be made arbitrarily large. Furthermore, we determine the hop independence numbers of some graphs including those resulting from some binary operations of graphs.

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How to Cite

Hassan, J., Canoy, Jr., S. R. ., & Aradais, A. A. . (2022). Hop Independent Sets in Graphs. European Journal of Pure and Applied Mathematics, 15(2), 467–477. https://doi.org/10.29020/nybg.ejpam.v15i2.4350