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On the Enumeration of Labeled Series-Parallel \(k \)-Cyclic \(2 \)-Connected Graphs

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Abstract

We deduce an explicit formula for the number of labeled series-parallel \(k \)-cyclic \(n \)-vertex \(2 \)-connected graphs and find the corresponding asymptotics for a large number of vertices and a fixed \(k \). Under the uniform probability distribution, an asymptotic formula is obtained for the probability that a random \(n \)-vertex \(k \)-cyclic \(2 \)-connected graph with a large number of vertices and a fixed \(k \) is a series-parallel graph.

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  1. All-Russian Institute for Scientific and Technical Information of Russian Academy of Sciences, Moscow, 125190, Russia

    V. A. Voblyi

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  1. V. A. Voblyi
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Correspondence to V. A. Voblyi.

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Translated by Ya.A. Kopylov

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Voblyi, V.A. On the Enumeration of Labeled Series-Parallel \(k \)-Cyclic \(2 \)-Connected Graphs. J. Appl. Ind. Math. 15, 169–174 (2021). https://doi.org/10.1134/S1990478921010154

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  • DOI: https://doi.org/10.1134/S1990478921010154

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