Let  be a graph. For each ordered subset  of V, each vertex  can be assigned a vector    of distances, which is denoted by  The set S is said to be a resolving set of G, if  for every    A resolving set of minimum cardinality is the metric basis and cardinality of a metric basis is the metric dimension of G. A dominating set Dis a locating dominating set if for each pair of vertices u, v in    where  The locating domination number  is the minimum cardinality of a locating dominating set for G. A vertex dominating set Dof Gcalled the metro dominating set whenever it also serves as a metric basis for G. The minimum cardinality of a metro dominating set is called metro domination number. Metro dominating set of a graph G also serves the purpose of locating dominating set of G, with fewer vertices. In this paper, we introduce the notion of unique metro domination sets and determine unique metro domination number of paths and cycles together with some bounds in general cases. Also, we show the existence of graphs whose order is up to four times their unique metro domination number, and end up with an open problem.

domination, metric dimension, metro domination, unique metro domination.