Journal of Applied Probability
- J. Appl. Probab.
- Volume 50, Number 2 (2013), 516-532.
Phase changes in the topological indices of scale-free trees
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.
J. Appl. Probab., Volume 50, Number 2 (2013), 516-532.
First available in Project Euclid: 19 June 2013
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Feng, Qunqiang; Hu, Zhishui. Phase changes in the topological indices of scale-free trees. J. Appl. Probab. 50 (2013), no. 2, 516--532. doi:10.1239/jap/1371648958. https://projecteuclid.org/euclid.jap/1371648958