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Power-law and log-periodic degree tails for a family of probability generating function equations arising in evolving networks
Qunqiang Feng, Xiao-Ming Fu, Tianyang Sun
For a fixed integer and , we study the probability generating function (pgf) equation \[ (1+2p)\,g(x)=2p\,x^{j}+g\bigl(x-px+px^{2}\bigr),\qquad 0\le x\le1 , \] which…
Limit Laws for the Distance to Fréchet Means of Random Graphs
Qunqiang Feng, Zixin Tang, Zhishui Hu
This paper investigates the Fréchet mean of the Erdős-Rényi random graph with respect to the Frobenius distance on graph Laplacians, a metric that captures global structu…
The generalized Zagreb index for non-plane and plane recursive trees
Qunqiang Feng, Michael Fuchs, Tsan-Cheng Yu
The Zagreb index, which is defined as the sum of squares of degrees of the nodes of a tree, was studied in previous works by martingale techniques for random non-plane recursive tr…
Limit laws for the generalized Zagreb indices of random graphs
Qunqiang Feng, Hongpeng Ren, Yaru Tian
In this paper, we study the limiting behavior of the generalized Zagreb indices of the classical Erdős-Rényi (ER) random graph , as . For any integer , w…