Eccentric connectivity index of fullerene graphs

Abstract

The eccentric connectivity index of the molecular graph is defined as $zeta^c(G)=sum_{uvin E}deg_G(u)ε(u)$ , where deg_G(x) denotes the degree of the vertex x in G and ε(u)=max{d(x,u) |x ε V(G)}. In this paper this polynomial is computed for an infinite class of fullerenes.