Geodesic
Symbolic method and directed graph enumeration
Élie de Panafieu1 ; Sergey Dovgal2 ; Élie de Panafieu ; Sergey Dovgal
1Nokia Bell Labs, France
2LIPN, Institut Galilée Université Paris, France
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 989-996 
Élie de Panafieu; Sergey Dovgal; Élie de Panafieu; Sergey Dovgal. Symbolic method and directed graph enumeration. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 989-996. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a98/
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     title = { Symbolic method and directed graph enumeration},
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     pages = {989--996},
     year = {2019},
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     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a98/}
}
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Voir la notice de l'article provenant de la source Comenius University

We introduce the arrow product, a systematic generating function technique for directed graph enumeration. It provides short proofs for previous results of Gessel on the number of directed acyclic graphs and of Liskovets, Robinson and Wright on the number of strongly connected directed graphs. We also recover Robinson’s enumerative results on directed graphs where all strongly connected components belong to a given family.