Geodesic
The number of labeled tetracyclic series-parallel~blocks
Prikladnaâ diskretnaâ matematika, no. 1 (2020), pp. 57-61.

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A series-parallel graph is a graph that does not contain a complete graph with four vertices as a minor. Such graphs are used in the construction of reliable communication networks. Let $TB(n)$ be the number of labeled series-parallel tetracyclic blocks with $n$ vertices. The formula $TB(n)=\dfrac{n!}{80640}(n^5+30n^4+257n^3+768n^2+960n+504)\dbinom{n-3}{3}$ is obtained. It is proved that with a uniform probability distribution, the probability that the labeled tetracyclic block is a series-parallel graph is asymptotically $3/11$.
Keywords: labeled graph, tetracyclic graph, series-parallel graph, block, enumeration, asymptotics. 
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V. A. Voblyi. The number of labeled tetracyclic series-parallel~blocks. Prikladnaâ diskretnaâ matematika, no. 1 (2020), pp. 57-61. http://geodesic.mathdoc.fr/item/PDM_2020_1_a4/

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