Count directed acyclic graphs of various sizes with specific characteristics.
a character string, the label describing the types of graphs to be counted (see below).
a vector of positive integers, the graph sizes as given by the numbers of nodes.
additional parameters (see below).
a boolean value. If
The types of graphs, and the associated additional parameters, are:
all-dags: all directed acyclic graphs.
dags-given-ordering: all directed acyclic graphs
with a specific topological ordering.
dags-with-k-roots: all directed acyclic graphs with
dags-with-r-arcs: all directed acyclic graphs with
count.graphs() returns an objects of class
bigz from the
gmp package, a vector with the graph counts.
Harary F, Palmer EM (1973). "Graphical Enumeration". Academic Press.
Rodionov VI (1992). "On the Number of Labeled Acyclic Digraphs". Discrete Mathematics, 105:319–321.
Liskovets VA (1976). "On the Number of Maximal Vertices of a Random Acyclic Digraph". Theory of Probability and its Applications, 20(2):401–409.
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