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Чеплюкова И.А.
Предельные теоремы для числа вершин заданной степени в условном конфигурационном графе
// Труды КарНЦ РАН. No 6. Сер. Математическое моделирование и информационные технологии. 2026. C. 114-126
Cheplyukova I.A. Limit theorems for the number of vertices with a given degree in а conditional configuration graph // Transactions of Karelian Research Centre of Russian Academy of Science. No 6. Mathematical Modeling and Information Technologies. 2026. Pp. 114-126
Keywords: configuration graph; vertex degree; limit distribution
We consider configuration graphs with N vertices. The vertex degrees are independent equally distributed random variables whose distribution satisfies the following condition: as k→∞
pk = P{η = k} ∼ h(k) / kg , 2 < g < 3,
where h(k) is a slowly varying function. We study the random graphs under the conditions that the sum of vertex degrees is n. The limit distributions of the number of vertices with a given degree in the conditional graph are obtained as N, n → ∞ and h(N)n2N(4−3g)/(g−1) ≥ C > 0 are obtained.
pk = P{η = k} ∼ h(k) / kg , 2 < g < 3,
where h(k) is a slowly varying function. We study the random graphs under the conditions that the sum of vertex degrees is n. The limit distributions of the number of vertices with a given degree in the conditional graph are obtained as N, n → ∞ and h(N)n2N(4−3g)/(g−1) ≥ C > 0 are obtained.
DOI: 10.17076/mat2327
Indexed at RSCI, RSCI (WS)
Last modified: July 3, 2026