Geodesic
Two combinatorial identities related to enumeration of graphs
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1, Tome 208 (2022), pp. 11-14.

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From the explicit formula for the number of labeled, series-parallel, $2$-connected graphs with a given number of vertices obtained by the author, two combinatorial identities are derived. Also, proofs of these identities independent of the enumeration of graphs are given.
Keywords: combinatorial identity, method of coefficients, enumeration, series-parallel graph, 2-connected graph. 
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V. A. Voblyi. Two combinatorial identities related to enumeration of graphs. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1, Tome 208 (2022), pp. 11-14. http://geodesic.mathdoc.fr/item/INTO_2022_208_a1/

[1] Voblyi V. A., Meleshko A. K., “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

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

[3] Voblyi V. A., “O perechislenii pomechennykh posledovatelno-parallelnykh $k$-tsiklicheskikh $2$-svyaznykh grafov”, Diskr. anal. issled. oper., 28:1 (2021), 7–14

[4] Zykov A. A., Osnovy teorii grafov, Nauka, M., 1987

[5] Leontev V. K., Izbrannye zadachi kombinatornogo analiza, Izd-vo MGTU im. N. E. Baumana, M., 2001

[6] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady. T. 1, Nauka, M., 1981 | MR

[7] 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

[8] Moon J. W., Counting Labelled Trees, Can. Math. Monogr., 1970 | MR | Zbl

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

[10] Wright E. M., “The number of connected sparsely edged graphs. II. Smooth graphs and blocks”, J. Graph Theory., 2:4 (1978), 299–305 | DOI | MR | Zbl