Geodesic
On the number of labeled outerplanar $k$-cyclic~bridgeless graphs
Diskretnyj analiz i issledovanie operacij, Tome 27 (2020) no. 1, pp. 5-16

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We obtain an explicit formula for the number of labeled connected outerplanar $k$-cyclic $n$-vertex bridgeless graphs. We find asymptotics for the number of those graphs for a large number of vertices and fixed $k$. As a consequence, we prove that, for $k$ fixed, almost all labeled connected outerplanar $k$-cyclic graphs have bridges. Tab. 1, bibliogr. 14.
Keywords: enumeration, labeled graph, outerplanar graph, bridgeless graph, $k$-cyclic graph, asymptotics. 
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     author = {V. A. Voblyi},
     title = {On the number of labeled outerplanar $k$-cyclic~bridgeless graphs},
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     publisher = {mathdoc},
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V. A. Voblyi. On the number of labeled outerplanar $k$-cyclic~bridgeless graphs. Diskretnyj analiz i issledovanie operacij, Tome 27 (2020) no. 1, pp. 5-16. http://geodesic.mathdoc.fr/item/DA_2020_27_1_a0/