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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2020, Volume 188, Pages 106–118
DOI: https://doi.org/10.36535/0233-6723-2020-188-106-118 (Mi into744) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On an approach to enumeration of labeled connected graphs: A review

V. A. Voblyi

All-Russian Institute for Scientific and Technical Information of Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.36535/0233-6723-2020-188-106-118
Abstract: The classical functional Riddell equation connects the generating functions of labeled connected graphs and their blocks. Using the Lagrange inversion theorem, the author obtained from this equation a formula, which is a convenient tool for the exact and asymptotic enumeration of labeled graphs in the case where the generating function of their blocks is known. This formula is valid for block-stable graph classes. A review of enumerative results obtained by using this approach for cacti, block-cactus graphs, Eulerian graphs, geodesic graphs, planar graphs, and series-parallel graphs is presented.
Keywords: enumeration, labeled graph, connected graph, block.
English version:
Journal of Mathematical Sciences (New York), 2025, Volume 287, Issue 6, Pages 920–933
DOI: https://doi.org/10.1007/s10958-025-07650-2
Document Type: Article
UDC: 519.175.3
MSC: 05С30
Language: Russian
Citation: V. A. Voblyi, “On an approach to enumeration of labeled connected graphs: A review”, Differential Equations and Mathematical Modeling, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 188, VINITI, Moscow, 2020, 106–118; J. Math. Sci. (N. Y.), 287:6 (2025), 920–933
Citation in format AMSBIB
\Bibitem{Vob20}
\by V.~A.~Voblyi
\paper On an approach to enumeration of labeled connected graphs: A review
\inbook Differential Equations and Mathematical Modeling
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 188
\pages 106--118
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into744}
\crossref{https://doi.org/10.36535/0233-6723-2020-188-106-118}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2025
\vol 287
\issue 6
\pages 920--933
\crossref{https://doi.org/10.1007/s10958-025-07650-2}
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