The reciprocal complementary Wiener number of graphs

Abstract

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