Reciprocal product–degree distance of graphs

Abstract

© 2016, University of Nis. All rights reserved. We investigate a new graph invariant named reciprocal product–degree distance, defined as: (Formula Presented) where deg(v) is the degree of the vertex v, and dist(u; v) is the distance between the vertices u and v in the underlying graph. RDD* is a product–degree modification of the Harary index. We determine the connected graph of given order with maximum RDD*-value, and establish lower and upper bounds for RDD*. Also a Nordhaus–Gaddum–type relation for RDD* is obtained.