On the metric dimension of corona product graphs

For an ordered set W = {w1, w2, · · · , wk} of vertices and a vertex v in a connected graph G, the representation of v with respect to W is the ordered k-tuple r(v|W ) = (d(v, w1), d(v, w2), · · · , d(v, wk)) where d(x, y) represents the distance between the vertices x and y. The set W is called a resolving set for G if every vertex of G has a distinct representation. A resolving set containing a minimum number of vertices is called a basis for G. The metric dimension of G, denoted by dim(G), is the number of vertices in a basis of G. A graph G corona H, G⊙H, is defined as a graph which formed by taking n copies of graphs H1, H2, · · · , Hn of H and connecting i-th vertex of G to the vertices of Hi. In this paper, we determine the metric dimension of corona product graphs G⊙H, the lower bound of the metric dimension of K1 +H and determine some exact values of the metric dimension of G⊙H for some particular graphs H.