Geodesic
On the limit distributions of the degrees of vertices in~configuration graphs with a~bounded number of edges
Sbornik. Mathematics, Tome 207 (2016) no. 3, pp. 400-417

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A model of a configuration graph on $N$ vertices is considered in which the degrees of the vertices are distributed identically and independently according to the law $\mathbf P\{\xi=k\}=k^{-\tau}-(k+1)^{-\tau}$, $k=1,2,\dots$, $\tau>0$, and the number of edges is no greater than $n$. Limit theorems for the number of vertices of a particular degree and for the maximum vertex degree as $N,n\to\infty$ are established. Bibliography: 18 titles.
Keywords: the number of vertices of a particular degree, the maximum vertex degree.
Mots-clés : configuration graph, limit distribution 
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     title = {On the limit distributions of the degrees of vertices in~configuration graphs with a~bounded number of edges},
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Yu. L. Pavlov; E. V. Khvorostyanskaya. On the limit distributions of the degrees of vertices in~configuration graphs with a~bounded number of edges. Sbornik. Mathematics, Tome 207 (2016) no. 3, pp. 400-417. http://geodesic.mathdoc.fr/item/SM_2016_207_3_a4/