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Enumeration of labeled nonplanar pentacyclic blocks
V. A. Voblyi All-Russian Institute for Scientific and Technical Information of Russian Academy of Sciences, Moscow
Abstract:
An planar graph is a graph that can be drawn on a plane without intersecting edges. A pentacyclic graph is a connected graph with $n$ vertices and $n + 4$ edges. We obtain an explicit formula for the number of labeled nonplanar pentacyclic blocks with a given number of vertices and found the corresponding asymptotics for the number of such graphs with a large number of vertices. We prove that under the uniform probability distribution, the probability that the labeled pentacyclic block is a nonplanar graph is asymptotically equal to $80/539$.
Keywords:
enumeration, labeled graph, block, planar graph, asymptotics, probability.
Citation:
V. A. Voblyi, “Enumeration of labeled nonplanar pentacyclic blocks”, Proceedings of the Voronezh spring mathematical school
“Modern methods of the theory of boundary-value problems. Pontryagin
readings – XXX”.
Voronezh, May 3-9, 2019. Part 4, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 193, VINITI, Moscow, 2021, 28–32
Linking options:
https://www.mathnet.ru/eng/into798 https://www.mathnet.ru/eng/into/v193/p28
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Abstract page: | 133 | Full-text PDF : | 48 | References: | 16 |
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