On the extremal connective eccentricity index among trees with maximum degree

The connective eccentricity index (CEI) of a graph G is defined as ξce(G)=∑v∈V(G)dG(v)εG(v), where dG(v) is the degree of v and εG(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.