Journal
| 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 |