The reciprocal complementary Wiener number of graphs

The reciprocal complementary Wiener number (RCW) of a connected graph G is defined as the sum ofweights frac{1}{D+1-d_G(x,y)} over all unordered vertex pairs in a graph G, where D is the diameter of Gand d_G(x,y) is the distance between vertices x and y. In this paper, we find new bounds for RCW ofgraphs, and study this invariant of two important types of graphs, named the Bar-Polyhex and theMycielskian graphs.