Eccentric Connectivity Index of Chemical Trees

TL;DR

This paper investigates the eccentric connectivity index of chemical trees, proving extremal properties for broom trees and providing an efficient algorithm for its calculation.

Contribution

It establishes extremal bounds for the eccentric connectivity index in chemical trees and introduces a linear-time algorithm for computing it.

Findings

Broom trees have maximum eccentric connectivity index among trees with fixed maximum degree.

Characterization of trees with minimum eccentric connectivity index.

Development of a simple linear algorithm for calculating the index.

Abstract

The eccentric connectivity index $\xi^c$ is a distance--based molecular structure descriptor that was recently used for mathematical modeling of biological activities of diverse nature. We prove that the broom has maximum $\xi^c$ among trees with a fixed maximum vertex degree, and characterize such trees with minimum $\xi^c$\,. In addition, we propose a simple linear algorithm for calculating $\xi^c$ of trees.