On the Metric Dimension of Join of a Graph with Empty Graph(Op)

For a graph G = (V, E), a set W⊂V is a resolving set if for each pair of distinct vertices v1,v2∈V there is a vertex w∈W such that d(v1,w)≠d(v2,w). A minimum resolving set or basis for G is a resolving set containing a minimum number of vertices and the cardinality of a minimum resolving set is called the metric dimension of G and is denoted by dim(G). In this paper, we investigates the metric dimension of Kn+Op, Pn+Op and K1,n+Op, where Op denotes the empty (isolated) graph of order p.