Relationships between Some Distance–Based Topological Indices

Abstract

The Harary index (HI), the average distance (AD), the Wiener polarity index (WPI) and the connective eccentricityindex (CEI) are distance-based graph invariants, some of which found applications in chemistry. We investigate the relationship between HI, AD, and CEI, and between WPI, AD, and CEI.

First, we prove that HI > AD for any connected graph and that HI > CEI for trees, with only three exceptions. We compare WPI with CEI for trees, and give a classification of trees for which CEI ≥ WPI or CEI < WPI. Furthermore, we prove that for trees, WPI > AD, with only three exceptions.