Reciprocal complementary Wiener numbers of trees, unicyclic graphs and bicyclic graphs

The reciprocal complementary Wiener number of a connected graph GG is defined as RCW(G)=∑{u,v}⊆V(G)1d+1−d(u,v|G) where V(G)V(G) is the vertex set, d(u,v|G)d(u,v|G) is the distance between vertices uu and vv, dd is the diameter of GG. We determine the trees with the smallest, the second smallest and the third smallest reciprocal complementary Wiener numbers, and the unicyclic and bicyclic graphs with the smallest and the second smallest reciprocal complementary Wiener numbers.