Geodesic
Asymptotic normality of the Zagreb index of random $b$-ary recursive trees
Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 1, pp. 91-101

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The $b$-ary recursive trees model is one of simple families of increasing trees. In this work, the Zagreb index $Z_n$ 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 expressions of the mean and variance of $Z_n$ are given. 
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     author = {Q. Feng and Hu Zhishui},
     title = {Asymptotic normality of the {Zagreb} index of random $b$-ary recursive trees},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
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     number = {1},
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Q. Feng; Hu Zhishui. Asymptotic normality of the Zagreb index of random $b$-ary recursive trees. Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 1, pp. 91-101. http://geodesic.mathdoc.fr/item/DVMG_2015_15_1_a8/