On the limit distributions of the degrees of vertices in configuration graphs with a bounded number of edges

摘要

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 P{xi = k} = k(-tau) - (k + 1)(-tau), k = 1, 2, ... , 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 -> infinity are established.