Extremal k-apex Trees for Randic Index

TL;DR

This paper investigates the Randic index in the context of k-apex trees, establishing new bounds and properties that enhance understanding of molecular structure descriptors.

Contribution

It proves that k-apex trees are not regular for k≥2 and introduces a sharp upper bound for their Randic index, advancing theoretical knowledge.

Findings

k-apex trees are not regular for k≥2

Established a sharp upper bound for the Randic index of k-apex trees

Extended previous bounds to a broader class of trees

Abstract

The Randic (connectivity) index is one of the most successful molecular descriptors in structure-property and structure-activity relationships studies. J. Gao found the sharp upper bound for the Randic index of apex trees. In this paper, we proved that k-apex trees are not regular graphs for k\ge2 and proposed a sharp upper bound for the Randic index of k-apex trees for k>1.