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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