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.
Citation
Qunqiang Feng. Zhishui Hu. "On the Zagreb index of random recursive trees." J. Appl. Probab. 48 (4) 1189 - 1196, December 2011. https://doi.org/10.1239/jap/1324046027
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