Geodesic
Asymptotic enumeration of labeled series-parallel $k$-cyclic bridgeless graphs
Diskretnyj analiz i issledovanie operacij, Tome 28 (2021) no. 4, pp. 61-69

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We deduce asymptotic formulas for the number of labeled connected series-parallel $k$-cyclic graphs with given order and fixed number $k$. We prove that almost all labeled series-parallel $k$-cyclic connected graphs without bridges for a fixed number of $k$ are blocks. Bibliogr. 17.
Keywords: enumeration, labeled graph, block, bridgeless graph, series-parallel graph, $k$-cyclic graph, asymptotics, random graph. 
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     author = {V. A. Voblyi},
     title = {Asymptotic enumeration of labeled series-parallel $k$-cyclic bridgeless graphs},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {61--69},
     publisher = {mathdoc},
     volume = {28},
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     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2021_28_4_a1/}
}
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V. A. Voblyi. Asymptotic enumeration of labeled series-parallel $k$-cyclic bridgeless graphs. Diskretnyj analiz i issledovanie operacij, Tome 28 (2021) no. 4, pp. 61-69. http://geodesic.mathdoc.fr/item/DA_2021_28_4_a1/