Distance k-Cost Effective Sets in the Corona and Lexicographic Product of Graphs

Let G be a connected graph and k ≥ 1 an integer. The open k-neighborhood Nk G(v) of v ∈ V (G) is the set = {u \ {v}: dG(u, v) ≤ k}. A S vertices called distance k-cost effective if for every vertex u in S, |Nk G(u) ∩ (V S)| − S| 0. maximum cardinality upper number G. In this paper, we characterized sets corona lexicographic product two graphs. Consequently, bounds or exact values numbers these graphs are obtained.