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Generalized de Bruijn digraphs. (English) Zbl 0654.05036

Consider the directed graphs with n labelled vertices and e edges. Let \(A_{n,e}\) denote the number of these graphs that are acyclic and let \(C_{n,e}\) denote the number that are weakly connected. Let \(a_{n,e}\) and \(c_{n,e}\) denote the corresponding numbers for unlabelled graphs. The authors show that \(A_{n,e}\sim C_{n,e}\sim n!a_{n,e}\sim n!C_{n,e}\) when \(\epsilon <2e/n(n-1)<1-\epsilon.\)
Reviewer: J.W.Moon

MSC:

05C20 Directed graphs (digraphs), tournaments
05C30 Enumeration in graph theory
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