On the connective eccentricity index of two types of trees

Abstract

The connective eccentricity index ${\xi }^{ce}={\sum }_{u\in V}^{}\frac{d(u)}{\epsilon (u)}$, where $\epsilon (u)$ 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.

arXiv admin note: text overlap with arXiv:1408.5865 by other authors