src/sage/graphs: Mark some doctests # optional - sage.groups

Author: Matthias Koeppe

src/sage/graphs/generators/families.py

@@ -2790,8 +2790,8 @@ def HanoiTowerGraph(pegs, disks, labels=True, positions=True):
 
     ::
 
-        sage: H = graphs.HanoiTowerGraph(3,4,labels=False,positions=False)
-        sage: H.automorphism_group().is_isomorphic(SymmetricGroup(3))
+        sage: H = graphs.HanoiTowerGraph(3, 4, labels=False, positions=False)
+        sage: H.automorphism_group().is_isomorphic(SymmetricGroup(3))           # optional - sage.groups
         True
         sage: H.chromatic_number()
         3

src/sage/graphs/generic_graph.py

@@ -18704,33 +18704,33 @@ def _color_by_label(self, format='hex', as_function=False, default_color="black"
         We consider the Cayley graph of the symmetric group, whose edges are
         labelled by the numbers 1,2, and 3::
 
-            sage: G = SymmetricGroup(4).cayley_graph()
-            sage: set(G.edge_labels())
+            sage: G = SymmetricGroup(4).cayley_graph()                                          # optional - sage.groups
+            sage: set(G.edge_labels())                                                          # optional - sage.groups
             {1, 2, 3}
 
         We first request the coloring as a function::
 
-            sage: f = G._color_by_label(as_function=True)
-            sage: [f(1), f(2), f(3)]
+            sage: f = G._color_by_label(as_function=True)                                       # optional - sage.groups
+            sage: [f(1), f(2), f(3)]                                                            # optional - sage.groups
             ['#0000ff', '#ff0000', '#00ff00']
-            sage: f = G._color_by_label({1: "blue", 2: "red", 3: "green"}, as_function=True)
-            sage: [f(1), f(2), f(3)]
+            sage: f = G._color_by_label({1: "blue", 2: "red", 3: "green"}, as_function=True)    # optional - sage.groups
+            sage: [f(1), f(2), f(3)]                                                            # optional - sage.groups
             ['blue', 'red', 'green']
-            sage: f = G._color_by_label({1: "red"}, as_function=True)
-            sage: [f(1), f(2), f(3)]
+            sage: f = G._color_by_label({1: "red"}, as_function=True)                           # optional - sage.groups
+            sage: [f(1), f(2), f(3)]                                                            # optional - sage.groups
             ['red', 'black', 'black']
-            sage: f = G._color_by_label({1: "red"}, as_function=True, default_color='blue')
-            sage: [f(1), f(2), f(3)]
+            sage: f = G._color_by_label({1: "red"}, as_function=True, default_color='blue')     # optional - sage.groups
+            sage: [f(1), f(2), f(3)]                                                            # optional - sage.groups
             ['red', 'blue', 'blue']
 
         The default output is a dictionary assigning edges to colors::
 
-            sage: G._color_by_label()
+            sage: G._color_by_label()                                                           # optional - sage.groups
             {'#0000ff': [((), (1,2), 1), ...],
              '#00ff00': [((), (3,4), 3), ...],
              '#ff0000': [((), (2,3), 2), ...]}
 
-            sage: G._color_by_label({1: "blue", 2: "red", 3: "green"})
+            sage: G._color_by_label({1: "blue", 2: "red", 3: "green"})                          # optional - sage.groups
             {'blue': [((), (1,2), 1), ...],
              'green': [((), (3,4), 3), ...],
              'red': [((), (2,3), 2), ...]}
@@ -18739,12 +18739,12 @@ def _color_by_label(self, format='hex', as_function=False, default_color="black"
 
         We check what happens when several labels have the same color::
 
-            sage: result = G._color_by_label({1: "blue", 2: "blue", 3: "green"})
-            sage: sorted(result)
+            sage: result = G._color_by_label({1: "blue", 2: "blue", 3: "green"})                # optional - sage.groups
+            sage: sorted(result)                                                                # optional - sage.groups
             ['blue', 'green']
-            sage: len(result['blue'])
+            sage: len(result['blue'])                                                           # optional - sage.groups
             48
-            sage: len(result['green'])
+            sage: len(result['green'])                                                          # optional - sage.groups
             24
         """
         if format is True:
@@ -21636,10 +21636,10 @@ def relabel(self, perm=None, inplace=True, return_map=False, check_input=True, c
         Relabeling using a Sage permutation::
 
             sage: G = graphs.PathGraph(3)
-            sage: from sage.groups.perm_gps.permgroup_named import SymmetricGroup
-            sage: S = SymmetricGroup(3)
-            sage: gamma = S('(1,2)')
-            sage: G.relabel(gamma, inplace=False).am()
+            sage: from sage.groups.perm_gps.permgroup_named import SymmetricGroup               # optional - sage.groups
+            sage: S = SymmetricGroup(3)                                                         # optional - sage.groups
+            sage: gamma = S('(1,2)')                                                            # optional - sage.groups
+            sage: G.relabel(gamma, inplace=False).am()                                          # optional - sage.groups
             [0 0 1]
             [0 0 1]
             [1 1 0]

src/sage/graphs/graph.py

@@ -601,8 +601,8 @@ class Graph(GenericGraph):
        'out' is the label for the edge on 2 and 5. Labels can be used as
        weights, if all the labels share some common parent.::
 
-        sage: a,b,c,d,e,f = sorted(SymmetricGroup(3))
-        sage: Graph({b:{d:'c',e:'p'}, c:{d:'p',e:'c'}})
+        sage: a, b, c, d, e, f = sorted(SymmetricGroup(3))              # optional - sage.groups
+        sage: Graph({b: {d: 'c', e: 'p'}, c: {d: 'p', e: 'c'}})         # optional - sage.groups
         Graph on 4 vertices
 
     #. A dictionary of lists::