Abstract :
Abstract. A set W V (G) is called a resolving set for G, if for each
two distinct vertices u; v 2 V (G) there exists w 2 W such that d(u;w)≠
d(v;w), where d(x; y) is the distance between the vertices x and y. The
minimum cardinality of a resolving set for G is called the metric dimension of G, and denoted by dim(G). In this paper, it is proved that in a connected graph G of order n which has a cycle, dim(G) ≤n-g(G)+2,
where g(G) is the length of the shortest cycle in G, and the equality holds if and only if G is a cycle, a complete graph or a complete bipartite graph Ks;t, s; t ≤2.
