University of KashanIranian Journal of Mathematical Chemistry2228-64895220141101The Eccentric Connectivity Index of Bucket Recursive Trees7783567110.22052/ijmc.2014.5671ENRaminKazemiImam Khomeini international universityJournal Article20130806If $G$ is a connected graph with vertex set $V$, then the eccentric connectivity index of $G$, $xi^c(G)$, is defined as $sum_{vin V(G)}deg(v)ecc(v)$ 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 random bucket recursive trees.https://ijmc.kashanu.ac.ir/article_5671_c75e8f8a191feb37be45cb549d22b33b.pdf