Abstract
We derive an asymptotic formula for the number of labeled connected series-parallel \( k \)-cyclic graphs of a large order with a fixed number \( k \). With a uniform probability distribution, we find the probability that a random labeled connected \( n \)-vertex \( k \)-cyclic graph with a fixed \( k \) as \( n\to \infty \) is a series-parallel graph. In addition, we determine the probability that, with a uniform probability distribution, a random labeled connected series-parallel \( n \)-vertex \( k \)-cyclic graph with a fixed \( k \) as \( n\to \infty \) is a cactus.
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Translated by V. Potapchouck
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Voblyi, V.A. On Asymptotic Enumeration of Labeled Series-Parallel \(k\)-Cyclic Graphs. J. Appl. Ind. Math. 16, 853–859 (2022). https://doi.org/10.1134/S199047892204024X
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DOI: https://doi.org/10.1134/S199047892204024X