Let be a strongly connected oriented graph with vertex-set and arc-set . The distance from a vertex to another vertex , , is the minimum length of oriented paths from to . Suppose is a nonempty ordered subset of . The representation of a vertex with respect to , , is defined as a vector . If any two distinct vertices satisfy , then is said to be a resolving set of . If the cardinality of is minimum, then is said to be a basis of , and the cardinality of is called the directed metric dimension of .
Let be the underlying graph of admitting a -covering. A -simple orientation is an orientation on such that every in is strongly connected. This paper deals with metric dimensions of oriented wheels, oriented fans, and amalgamation of oriented cycles, all of which admit -simple orientations.