On the Maximal Degree of a Vertex of a Conditional Configuration Graph

We consider the model of an N-vertex configuration graph, where the degrees of vertices are independent and identically distributed random variables, and the distribution of the random variable η, which is the degree of each vertex, satisfies the condition pₖ=P\η=k\~ h(k)/kᵍ, $2<g<3$, k→∞, where $h(x)$ is a function which slowly varies at infinity. We prove the limit theorem for the maximal degree of vertices in this configuration graph provided that the number n of edges in the graph is known, N, n→∞, and h(N)n²N(4-3g)/(g-1) C>0.