id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5658	Anoche, Jesica; Canoy, Jr., Sergio	Another Look at Hop Independence in Graphs	2025	15	.pdf	application/pdf	6820	588	91	= n if and only if G = Kn; and (ii) for n ≥ 3, αh(G) = n− 1 if and only if G ̸= Kn and there exists v ∈ V (G) such that G \ v = Kn−1. Observation 1: Let G be a graph of order n. (i) ∅ and cliques in G are hop independent sets. (iii) S = SG1 ∪ SG2 ∪ I1 ∪ I2 and satisfies the following conditions: (a) I1 ⊆ I(G1) and I2 ⊆ I(G2). (b) SG1 and SG2 are hop independent sets in G1 and G2, respectively, not containing isolated vertices.	cache/ejpam-5658.pdf	txt/ejpam-5658.txt