Unique basis graphs.

A set W subset of V (G) is called a resolving set, if for each two distinct vertices u, v is an element of V(G) there exists w is an element of W such that d(u,w) not equal d(v, w), where d(x, y) is the distance between the vertices x and y. A resolving set for G with minimum cardinality is called a metric basis. A graph with a unique metric basis is called a unique basis graph. In this paper, we study some properties of unique basis graphs.