Abstract
A vertex x of a connected graph G resolves two distinct vertices u and v in V(G) if the distance between u and x differs from the distance between v and x. A subset X of V(G)resolves two distinct vertices u and v in G if there exists a vertex x in X that resolves u and v; X is a metric generator of G if, for every pair of distinct vertices u and v of G, X resolves u and v and is a metric basis of G if X is a metric generator of G with minimum cardinality. The metric dimension of G is the cardinality of a metric basis of G. The problem of finding the metric dimension of an arbitrary graph is NP-hard. In this paper we show that the problem is solvable in linear time for the class of bipartite distance-hereditary graphs.
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