On the locating-chromatic number of corona product of graphs

Let G= (V, E) be a finite, simple, and connected graph. The locating-chromatic number of a graph G can be defined as the cardinality of a minimum resolving partition of the vertex set V (G) such that all vertices have different coordinates and every two adjacent vertices in G is not contained in the same partition class. In this case, the coordinate of a vertex in G is expressed in terms of the distances of this vertex to all partition classes. The corona product of a graph G of order n and a graph H, denoted by G H, is the graph obtained by taking one copy of G and n copies of H and joining the i^th-vertex of G to every vertex in the i^th-copy of H. In this paper, we determine the sharp general bound of the locating-chromatic number of G H for G is a connected graph and H is an arbitrary graph, or G is a tree graph and H is a complement of complete graph.