id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5973	Hamja, Jamil; Sheikholeslami, Seyed Mahmoud ; Imelda, Aniversario; Cabardo, Lyster Rey	Hop $k$-Rainbow Domination in Graphs	2025	17	.pdf	application/pdf	7243	606	87	Applying the bounds presented in Theorem 4, for any positive integer k ≥ 1 and every graph G of order n, we have that 2min{n, k + 1} ≤ γhrk(G) + γhrk(G) ≤ 2n. = { k, if n ≥ k, n, if n < k. Proposition 3.	cache/ejpam-5973.pdf	txt/ejpam-5973.txt