Geodesic
On enumeration of labeled connected bridgeless graphs
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 4, Tome 223 (2023), pp. 138-147

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In this paper, we obtain explicit formulas and asymptotics for some classes of bridgeless labeled graphs: cacti, block graphs, block-cactus graphs, and series-parallel graphs. We prove that, under a uniform probability distribution, almost all graphs from the classes considered have bridges.
Keywords: enumeration, labeled graph, $k$-cyclic graph, block, bridge, bridgeless graph, Eulerian graph, series-parallel graph, asymptotics, random graph. 
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     title = {On enumeration of labeled connected bridgeless graphs},
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V. A. Voblyi. On enumeration of labeled connected bridgeless graphs. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 4, Tome 223 (2023), pp. 138-147. http://geodesic.mathdoc.fr/item/INTO_2023_223_a13/