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 ξce(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.