Geodesic
On the enumeration of labeled series-parallel $k$-cyclic $2$-connected graphs
Diskretnyj analiz i issledovanie operacij, Tome 28 (2021) no. 1, pp. 5-14

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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. Tab. 1, bibliogr. 11.
Keywords: enumeration, labeled graph, series-parallel graph, $k$-cyclic graph, asymptotics, random graph. 
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     title = {On the enumeration of labeled series-parallel $k$-cyclic $2$-connected graphs},
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V. A. Voblyi. On the enumeration of labeled series-parallel $k$-cyclic $2$-connected graphs. Diskretnyj analiz i issledovanie operacij, Tome 28 (2021) no. 1, pp. 5-14. http://geodesic.mathdoc.fr/item/DA_2021_28_1_a0/