Symbolic method and directed graph enumeration

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Élie de Panafieu Sergey Dovgal


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.

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de Panafieu, ., & Dovgal, S. (2019). Symbolic method and directed graph enumeration. Acta Mathematica Universitatis Comenianae, 88(3), 989-996. Retrieved from