University of Isfahan Transactions on Combinatorics 2251-8657 10 4 2021 12 01 On the extremal connective eccentricity index among trees with maximum degree 239 246 25656 10.22108/toc.2021.120679.1693 EN Fazal Hayat School of Mathematical Sciences, South China Normal University, Guangzhou 510631, PR China Journal Article 2019 12 23 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. https://toc.ui.ac.ir/article_25656_ce36f15a7dee2e1ace7fdfcaf03f97ae.pdf