LAUSR

Let G be a finite connected graph. The eccentric connectivity index ξc(G) of G is defined as ξc(G) = ΣV∈V (G) ec(v)deg(v), where ec(v) and deg(v) denote the eccentricity and degree of a vertex v in G, respectively. In this paper, we give an asymptotically sharp upper bound on the eccentric connectivity index in terms of order and vertex-connectivity and in terms of order and edge-connectivity. We also improve the bounds for triangle-free graphs.