Several topological indces of random binary trees

Chongliang Luo, Qunqiang Feng, Shuguang Zhang

Research output: Contribution to journalArticlepeer-review


The Zagreb index of random binary trees was mainly investigated under three standard probability models: random binary search trees, random Catalan trees and random digital search trees. Using an alternative method to study the number of leaves, the exact mean and variance of the Zagreb index of a random binary search tree was first obtained. After that, the asymptotic normality was derived by the contraction method. Then, the asymptotic normality for the Zagreb index of a random Catalan tree and a digital search tree were also given. Finally, two other topological indices named the Gordon-Scantlebury and Piatt indices, both closely related to the Zagreb index, were discussed in passing.

Original languageEnglish
Pages (from-to)967-974
Number of pages8
JournalJournal of University of Science and Technology of China
Issue number12
StatePublished - 2013


  • Binary search trees
  • Catalan trees
  • Contraction method
  • Digital search trees
  • Random tree
  • Topological index


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