On the locating domination number of corona product

Abstract

Let G =(V (G),E(G) be a connected graph and v V (G). A dominating set for a graph G =(V, E) is a subset D of V such that every vertex not in D is adjacent to at least one member of D. The domination number γ(G) is the number of vertices in a smallest dominating set for G. Vertex set S in graph G =(V, E) is a locating dominating set if for each pair of distinct vertices u and v in V (G) − S we have N(u) ∩ S = φ, N(v) ∩ S = φ,andN(u) ∩ S = N(v) ∩ S, that is each vertex outside of S is adjacent to a distinct, nonempty subset of the elements of S. In this paper, we characterize the locating dominating sets in the corona product of graphs namely path, cycle, star, wheel, and fan graph.