## Journal of Applied Probability

### On the Zagreb index of random recursive trees

#### Abstract

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

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

Dates
First available in Project Euclid: 16 December 2011

https://projecteuclid.org/euclid.jap/1324046027

Digital Object Identifier
doi:10.1239/jap/1324046027

Mathematical Reviews number (MathSciNet)
MR2896676

Zentralblatt MATH identifier
1234.05053

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

#### Citation

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. https://projecteuclid.org/euclid.jap/1324046027

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