On the connective eccentricity index of trees and unicyclic graphs with given diameter

The connective eccentricity index (CEI) of a graph G is defined as ξ ce ( G ) = ∑ v ∈ V ( G ) d ( v ) ε ( v ) , where ε ( v ) , d ( v ) denote the eccentricity and the degree of v, respectively. In this paper we investigate the connective eccentricity index of trees and unicyclic graphs on n vertices with diameter d. We also characterize the extremal graphs.