A New Method for Computing the Eccentric Connectivity Index of Fullerenes

ACM Computing Classification System (1998): G.2.2, G.2.3.

The eccentric connectivity index of the molecular graph G, ξ^c (G), was proposed by Sharma, Goswami and Madan. It is defined as ξ^c (G) = Σu∈V(G)degG(u) ecc(u), where degG(x) denotes the degree of the vertex x in G and ecc(u) = Max{d(x, u) | x ∈ V (G)}. In this paper this graph invariant is computed for an infinite class of fullerenes by means of group action.