Geodesic
New identities from enumeration of graphs
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 3, Tome 229 (2023), pp. 33-36.

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In this paper, three new combinatorial identities related to the enumeration of labeled connected graphs with a given number of endpoints are presented. We give a proof of these identities independent of the enumeration of graphs. For one of the identities, a course of the proof based on formulas for enumerating graphs is outlined.
Keywords: combinatorial identity, enumeration, labeled graph, connected graph, endpoint
Mots-clés : unicyclic graph. 
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V. A. Voblyi. New identities from enumeration of graphs. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 3, Tome 229 (2023), pp. 33-36. http://geodesic.mathdoc.fr/item/INTO_2023_229_a3/

[1] Voblyi V. A., “Asimptoticheskoe perechislenie pomechennykh svyaznykh razrezhennykh grafov s zadannym chislom visyachikh vershin”, Metody diskretnogo analiza v teorii grafov i skhem, 42 (1985), 3–14

[2] Voblyi V. A., “Ob odnom tozhdestve dlya mnogochlenov Kravchuka”, Mat. XX Mezhdunar. semin. «Kombinatornye konfiguratsii i ikh prilozheniya» (Kropivnitskii, 13–14 aprelya 2018 g.), Kropivnitskii, 2018

[3] Voblyi V. A., “O kombinatornom tozhdestve, svyazannom s perechisleniem grafov”, Mat. XXI Mezhdunar. semin. «Kombinatornye konfiguratsii i ikh prilozheniya» (Kropivnitskii, 17–18 maya 2019 g.), Kropivnitskii, 2019, 30–31

[4] Voblyi V. A., “Dva kombinatornykh tozhdestva, svyazannykh s perechisleniem grafov”, Itogi nauki tekhn. Sovrem. mat. prilozh. Temat. obz., 208 (2022), 11–14

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

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

[7] Prudnikov A. P. i dr., Integraly i ryady. T. 1, M., 1981

[8] Koutras M., “Non-central Stirling numbers and some applications”, Discr. Math., 42 (1982), 73–80

[9] Moon J. W. Connected graphs with unlabeled end-points, J. Comb. Theory., 6 (1969), 65–66

[10] Moon J. W., Counting Labelled Trees, Can. Math. Congr., 1970