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2020 ◽  
Author(s):  
L. Indriati ◽  
M. A. Nugraha ◽  
Y. S. Perng
Keyword(s):  
Free Tree

Phase Changes in the Topological Indices of Scale-Free Trees

2013 ◽  
Vol 50 (02) ◽  
pp. 516-532 ◽  
Author(s):  
Qunqiang Feng ◽  
Zhishui Hu
Keyword(s):  
Nonnegative Integer ◽  
Topological Indices ◽  
Critical Values ◽  
Phase Changes ◽  
Zagreb Index ◽  
Asymptotic Behaviors ◽  
Scale Free ◽  
Recursive Tree ◽  
Free Tree ◽  
Recursive 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.

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