The Wiener index is the sum of distances between all pairs of vertices of a (connected) graph. In this paper, we define two novel graph invariants: the inverted distance and the inverted Wiener index. The inverted distance between any two different vertices uand vof a simple connected graph G is defined as:  where Ddenotes the diameter of Gand  denotes the distance of the vertices uand v. The inverted Wiener index of a simple connected graph G is defined as:  where the sum is taken over unordered pairs of vertices of G. We characterized maximum trees with respect to the inverted Wiener index.

inverted distance, inverted Wiener index, Wiener index, average inverted distance.