Journal of Applied Probability

On the Zagreb index of random recursive trees

Qunqiang Feng and Zhishui Hu

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We investigate the Zagreb index, one of the topological indices, of random recursive trees in this paper. Through a recurrence equation, the first two moments of Zn, the Zagreb index of a random recursive tree of size n, are obtained. We also show that the random process {Zn - E[Zn], n ≥ 1} is a martingale. Then the asymptotic normality of the Zagreb index of a random recursive tree is given by an application of the martingale central limit theorem. Finally, two other topological indices are also discussed in passing.

Article information

J. Appl. Probab., Volume 48, Number 4 (2011), 1189-1196.

First available in Project Euclid: 16 December 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C05: Trees 60C05: Combinatorial probability
Secondary: 60F05: Central limit and other weak theorems

Random tree Zagreb index recursive tree martingale central limit theorem


Feng, Qunqiang; Hu, Zhishui. On the Zagreb index of random recursive trees. J. Appl. Probab. 48 (2011), no. 4, 1189--1196. doi:10.1239/jap/1324046027.

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