Title |
Hop Independent Sets in Graphs
**Posted by** Sergio Jr. Canoy |

Authors |
Hassan, Javier; Canoy, Sergio Jr.; Aradais, Alkajim |

Publication date |
2022/4 |

Journal |
European Journal of Pure and Applied Mathematics |

Volume |
15 |

Issue |
2 |

Pages |
467-477 |

Publisher |
New York Business Global |

Abstract |
Let G be an undirected graph with vertex and edge sets V (G) and E(G), respectively.
A subset S of 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, d(v,w) is not equal to 2 for any distinct vertices v and w in S. The maximum
cardinality of a hop independent set of G, denoted by$alpha_h(G)$, 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. |

Index terms / Keywords |
hop independence, hop dominating, join, corona, lexicographic product |