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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     author = {V. A. Voblyi},
     title = {Two combinatorial identities related to enumeration of graphs},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {11--14},
     publisher = {mathdoc},
     volume = {208},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_208_a1/}
}
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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/