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1 results

  • Phase Changes in the Topological Indices of Scale-Free Trees

  • Part of
  • Qunqiang Feng, Zhishui Hu
  • Journal:
    Journal of Applied Probability / Volume 50 / Issue 2 / June 2013
    Published online by Cambridge University Press:
    30 January 2018, pp. 516-532
    Print publication:
    June 2013
    • Article
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  • 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.