Fazal Hayat - School of Mathematical Sciences, South China Normal University, Guangzhou ۵۱۰۶۳۱, PR China

The connective eccentricity index (CEI) of a graph G is defined as \xi^{ce}(G)=\sum_{v \in V(G)}\frac{d_G(v)}{\varepsilon_G(v)}, where d_G(v) is the degree of v and \varepsilon_G(v) is the eccentricity of v. In this paper, we characterize the unique trees with the maximum and minimum CEI among all n-vertex trees and n-vertex conjugated trees with fixed maximum degree, respectively.

Connective eccentricity index, tree, maximum degree, perfect matching