id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5205	Fortosa, Rona Jane Gamayot; Jamil, Ferdinand; Canoy, Sergio	Convex Roman Dominating Functions on Graphs under some Binary Operations	2024	17	.pdf	application/pdf	9480	658	92	Then f = (V0, V1, V2) is a CvRDF on G ◦H if and only if each of the following conditions hold: (i) V0 ∩ V (G) = ∅ (ii) For each v ∈ V2 ∩ V (G), Sv 1 ∪ Sv 2 induces a complete subgraph of Hv or V (Hv) \ (Sv 1 ∪ Sv 2 ) is a non-connecting set in Hv. (iii) For each v ∈ V1∩V (G) such that Sv 1 ̸= V (Hv), Sv 2 ̸= ∅, Sv 0 ⊆ NHv(Sv 2 ), and Sv 1 ∪Sv 2 induces a complete subgraph of Hv or V (Hv) \ (Sv 1 ∪ Sv 2 ) is a non-connecting set in Hv and Proof. Let f = (V0, V1, V2) be a CvRDF of G ◦ H. Since V1 ∪ V2 is a dominating set of G ◦H, V (v +Hv) ∩ (V1 ∪ V2) ̸= ∅ (1) R. Fortosa, S. Canoy Jr. / Eur.	cache/ejpam-5205.pdf	txt/ejpam-5205.txt