Phase Changes in the Topological Indices of Scale-free Trees

FENG Qunqiang; HU Zhishui

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Phase Changes in the Topological Indices of Scale-free Trees

FENG Qunqiang,HU Zhishui * #

University of Science and Technology of China, HeFei 230026

*Correspondence author

#Submitted by

Subject:

Funding: the NSFC（No.No.10801122）, Research Fund for theDoctoral Program of Higher Education of China（No.No.200803581009 and No.20093402120014）

Opened online:13 February 2012

Accepted by: none

Citation: FENG Qunqiang,HU Zhishui.Phase Changes in the Topological Indices of Scale-free Trees[OL]. [13 February 2012] http://en.paper.edu.cn/en_releasepaper/content/4462894

A scale-free tree with the parameter β is very close to a star if βis just a bit larger than -1, whereas it is close to a randomrecursive tree if β is very large. Through the Zagreb index, the whole scene of the evolution of the scale-free trees model is consideredas β goes from -1 to +∞. And the first two moments and the asymptotic behaviors of this index of a scale-free tree are obtained for all β>-1.

Keywords:Limit theory; Random networks; small-world; Zagreb index; scale-free trees

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