On the extremal connective eccentricity index among trees with maximum degree

Document Type : Research Paper


School of Mathematical Sciences, South China Normal University, Guangzhou 510631, 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.


Main Subjects

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Volume 10, Issue 4 - Serial Number 4
December 2021
Pages 239-246
  • Receive Date: 23 December 2019
  • Revise Date: 03 May 2021
  • Accept Date: 05 May 2021
  • Published Online: 01 December 2021