We consider configuration graphs under the condition that the sum of vertex degrees is bounded from above by n. The vertex degrees are independent identically distributed random variables. The distribution of the vertex degree ξ is unknown and has the only limiting condition that
P{ξ=k} пропорционально d/( k^g ln ^h k),
where d>0, g>1, h≥0.
We obtained the limit distributions of the maximum vertex degree as the number of graph vertices and n tends to infinity.