Let G=(V,E) be a connected graph. The eccentric connectivity index of G is defined by ξC(G)=∑ u∈V(G)deg(u)e(u), where deg(u) and e(u) denote the degree and eccentricity of the vertex u in G, respectively. In this paper, we introduce a new formulation of ξC that will be called the distance eccentric connectivity index of G and defined by ξDe(G)=∑ u∈V(G)degDe(u)e(u) where degDe(u) denotes the distance eccentricity degree of the vertex u in G. The aim of this paper is to introduce and study this new topological index. The values of the eccentric connectivity index is calculated for some fundamental graph classes and also for some graph operations. Some inequalities giving upper and lower bounds for this index are obtained.

Keywords: eccentric connectivity index, distance eccentric connectivity index, topological graph index, graph operation.