Far Eastern Mathematical Journal

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Asymptotic normality of the Zagreb index of random b-ary recursive trees


Qunqiang Feng, Zhishui Hu

2015, issue 1, . 91-101


Abstract
The b-ary recursive trees model is one of simple families of increasing trees. In this work, the Zagreb index Zn of a random b-ary recursive tree of size n is studied. As $n\to\infty$, the asymptotic normality of $Z_n$ is established through the martingale central limit theorem, as well as the asymptotic expressionsof the mean and variance of $Z_n$ are given.

Keywords:
random tree, Zagreb index, martingale, asymptotic normality

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References

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