enable the generation of acyclic orientations with nauty_directg

Author: dcoudert

src/sage/graphs/digraph_generators.py

@@ -649,14 +649,16 @@ def nauty_directg(self, graphs, options="", debug=False):
 
         INPUT:
 
-        - ``graphs`` -- a :class:`Graph` or an iterable containing :class:`Graph`
-          the graph6 string of these graphs is used as an input for ``directg``.
+        - ``graphs`` -- a :class:`Graph` or an iterable containing
+          :class:`Graph`.  The graph6 string of these graphs is used as an input
+          for ``directg``.
 
         - ``options`` (str) -- a string passed to directg as if it was run at
           a system command line. Available options from directg --help::
 
             -e<int> | -e<int>:<int>  specify a value or range of the total number of arcs
             -o       orient each edge in only one direction, never both
+            -a       only make acyclic orientations (implies -o)
             -f<int>  Use only the subgroup that fixes the first <int> vertices setwise
             -V       only output graphs with nontrivial groups (including exchange of
                      isolated vertices).  The -f option is respected.
@@ -680,6 +682,19 @@ def nauty_directg(self, graphs, options="", debug=False):
             sage: len(list(digraphs.nauty_directg(graphs.PetersenGraph(), options="-o")))
             324
 
+        Generate non-isomorphic acyclic orientations::
+
+            sage: K = graphs.CompleteGraph(4)
+            sage: all(d.is_directed_acyclic() for d in digraphs.nauty_directg(K, options='-a'))
+            True
+            sage: sum(1 for _ in digraphs.nauty_directg(K, options='-a'))
+            1
+            sage: S = graphs.StarGraph(4)
+            sage: all(d.is_directed_acyclic() for d in digraphs.nauty_directg(S, options='-a'))
+            True
+            sage: sum(1 for _ in digraphs.nauty_directg(S, options='-a'))
+            5
+
         TESTS::
 
             sage: g = digraphs.nauty_directg(graphs.PetersenGraph(), options="-o -G")