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June 2013 Phase changes in the topological indices of scale-free trees
Qunqiang Feng, Zhishui Hu
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J. Appl. Probab. 50(2): 516-532 (June 2013). DOI: 10.1239/jap/1371648958

Abstract

A scale-free tree with the parameter β is very close to a star if β is just a bit larger than -1, whereas it is close to a random recursive tree if β is very large. Through the Zagreb index, we consider the whole scene of the evolution of the scale-free trees model as β goes from -1 to + ∞. The critical values of β are shown to be the first several nonnegative integer numbers. We get the first two moments and the asymptotic behaviors of this index of a scale-free tree for all β. The generalized plane-oriented recursive trees model is also mentioned in passing, as well as the Gordon-Scantlebury and the Platt indices, which are closely related to the Zagreb index.

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Qunqiang Feng. Zhishui Hu. "Phase changes in the topological indices of scale-free trees." J. Appl. Probab. 50 (2) 516 - 532, June 2013. https://doi.org/10.1239/jap/1371648958

Information

Published: June 2013
First available in Project Euclid: 19 June 2013

zbMATH: 1267.05065
MathSciNet: MR3102497
Digital Object Identifier: 10.1239/jap/1371648958

Subjects:
Primary: 05C05, 60C05
Secondary: 60F05

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 2 • June 2013
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