# On the connective eccentricity index of two types of trees

## TL;DR

This paper investigates the extremal values of the connective eccentricity index in trees, identifying those with minimal and maximal indices under specific structural constraints such as degree sequences and number of branching vertices.

## Contribution

It provides a comprehensive characterization of extremal trees for the connective eccentricity index based on degree sequence and branching vertices.

## Key findings

- Identified trees with extremal connective eccentricity index for given degree sequences.
- Determined extremal trees with minimal and maximal index for fixed number of branching vertices.

## Abstract

The connective eccentricity index $\xi^{ce}=\sum^{}_{u\in V}\frac{d(u)}{\varepsilon(u)}$, where $\varepsilon(u)$ and $d(u)$ denote the eccentricity and the degree of the vertex $u$, respectively. In this paper, we first determine the extremal trees which minimize and maximize the connective eccentricity index among all trees with a given degree sequence, and then determine the extremal trees which minimize and maximize the connective eccentricity index among all trees with a given number of branching vertices.