The Eccentric Connectivity Index of Bucket Recursive Trees

If g is a connected graph with vertex set v , then the eccentric connectivity index of g , ξ^c (g) , is defined as σv∈v (g)^deg(v)ecc(v) where deg(v) is the degree of a vertex v and ecc(v) is its eccentricity. in this paper we show some convergence in probability and an asymptotic normality based on this index in two classes of random bucket recursive trees.