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The asymptotic degree distribution of a kind of evolving random tree

In this paper, we introduce an evolving random tree; the model is a combination of a preferential attachment model and a uniform model. We show that the distribution of the number of leaves at time n is approximated by the Poisson distribution with parameter , the proportional degree sequence obeys a power law with parameter and α is a constant number that describes the probability of choosing the connecting form in the evolving random tree model.