A new formula for the number of labeled series-parallel 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 Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 4, Tome 182 (2020), pp. 10-13.

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A series-parallel graph is a graph that does not contain a complete graph with 4 vertices as a minor. A new explicit simpler formula for the number of labeled series-parallel 2-connected graphs with a given number of vertices is obtained.
Keywords: enumeration, labeled graph, series-parallel graph, 2-connected graph
Mots-clés : explicit formula.
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V. A. Voblyi. A new formula for the number of labeled series-parallel 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 Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 4, Tome 182 (2020), pp. 10-13. http://geodesic.mathdoc.fr/item/INTO_2020_182_a1/

[3] Voblyi V. A., “Vtoroe sootnoshenie Riddela i sledstviya iz nego”, Diskr. anal. issl. oper., 26:1 (2019), 20–32 | Zbl

[4] Voblyi V. A., “Chislo pomechennykh posledovatelno-parallelnykh tetratsiklicheskikh blokov”, Prikl. diskr. mat., 2020, no. 47, 57–61

[5] Voblyi V. A., “Yavnaya formula dlya chisla pomechennykh posledovatelno-parallelnykh $k$-tsiklicheskikh blokov”, Mat. zametki., 108:4 (2020), 622–624 | MR

[6] Voblyi V. A., Meleshko A. M., “O chisle pomechennykh posledovatelno-parallelnykh tritsiklicheskikh blokov”, Mat. XV Mezhdunar. konf. «Algebra, teoriya chisel i diskretnaya geometriya. Sovremennye problemy i prilozheniya» (Tula, 28-31 maya 2018 g.), TPGU, Tula, 168–170

[7] Lavrentev M. A., Shabat B. V., Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1965

[8] Bodirsky M., Gimenez O., Kang M., Noy M., “Enumeration and limit laws of series-parallel graphs”, Eur. J. Combin., 28:8 (2007), 2091–2105 | DOI | MR | Zbl

[9] Radhavan S., “Low-connectivity network design on series-parallel graphs”, Networks., 43:3 (2004), 163–176 | DOI | MR