Itogi Nauki i Tekhniki. Seriya "Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory"
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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2020, Volume 188, Pages 106–118 (Mi into744)  

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

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

DOI: https://doi.org/10.36535/0233-6723-2020-188-106-118

Full text: PDF file (243 kB)
References: PDF file   HTML file

UDC: 519.175.3
MSC: 05С30

Citation: V. A. Voblyi, “On an approach to enumeration of labeled connected graphs: A review”, Differential Equations and Mathematical Modeling, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 188, VINITI, Moscow, 2020, 106–118

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. Ser. 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}


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