AbstractA vertex v in a simple connected graph G resolves two vertices x and y in G if the distance from x to v is not equal to distance from y to v. The vertex set R{x, y} is defined as the set of vertices in G which resolve x and y. A function f : V(G) → [0,1] is called a resolving function of G if f (R{x, y}) ≥ 1 for any two distinct vertices x and y in G. The minimal value of f (V(G)) for all resolving functions f of G is called the fractional metric dimension of G. In this paper, we determine the fractional metric dimension of Gwhere G is a tree or G is a unicyclic graph.