The Metric Dimension of Graph with Pendant Edges

For an ordered set W = {w_1,w_2,...,w_k} of vertices and a vertex \nv in a connected graph G, the representation of v with respect to \nW is the ordered k-tuple r(v|W) = (d(v,w_1), d(v,w_2),..., d(v,w_k)) \nwhere d(x,y) represents the distance between the vertices x and y. \nThe set W is called a resolving set for G if every two vertices of G \nhave distinct representations. A resolving set containing a minimum \nnumber of vertices is called a basis for G. The dimension of G, \ndenoted by dim(G), is the number of vertices in a basis of G. In this \npaper, we determine the dimensions of some corona graphs G⊙K_1, \nand G⊙K_m for any graph G and m ≥ 2, and a graph with pendant \nedges more general than corona graphs G⊙K_m.