An acyclic digraph is a directed graph containing no directed cycles, also known as a directed acyclic graph or a "DAG."
Every finite acyclic digraph has at least one node of outdegree
0. The numbers of acyclic digraphs on , 2, ... vertices are 1, 2, 6, 31, 302, 5984, ... (OEIS A003087).
The numbers of labeled acyclic digraphs on , 2, ... nodes are 1, 3, 25, 543, 29281, ... (OEIS A003024).
Weisstein's conjecture proposed that positive eigenvalued-matrices were in one-to-one
correspondence with labeled acyclic digraphs on nodes, and this was subsequently proved by McKay et al.
(2004). Counts for both are therefore given by the beautiful recurrence
equation
with
(Harary and Palmer 1973, p. 19; Robinson 1973, pp. 239-273).
, 2, ... vertices are 1, 2, 6, 31, 302, 5984, ... (OEIS A003087).
, 2, ... nodes are 1, 3, 25, 543, 29281, ... (OEIS A003024).
Weisstein's conjecture proposed that positive eigenvalued 
-matrices were in one-to-one
correspondence with labeled acyclic digraphs on 
nodes, and this was subsequently proved by McKay et al.
(2004). Counts for both are therefore given by the beautiful recurrence
equation
(Harary and Palmer 1973, p. 19; Robinson 1973, pp. 239-273).
-Matrices." J. Integer Sequences 7,
Article 04.3.3, 1-5, 2004.