def Path(self, n):
r"""
Returns a directed path on `n` vertices.
INPUT:
- ``n`` (integer) -- number of vertices in the path.
EXAMPLES::
sage: g = digraphs.Path(5)
sage: g.vertices()
[0, 1, 2, 3, 4]
sage: g.size()
4
sage: g.automorphism_group().cardinality()
1
"""
g = DiGraph(n)
g.name("Path")
if n:
g.add_path(range(n))
g.set_pos({i: (i, 0) for i in range(n)})
return g
def Path(self,n):
r"""
Returns a directed path on `n` vertices.
INPUT:
- ``n`` (integer) -- number of vertices in the path.
EXAMPLES::
sage: g = digraphs.Path(5)
sage: g.vertices()
[0, 1, 2, 3, 4]
sage: g.size()
4
sage: g.automorphism_group().cardinality()
1
"""
if n<0:
raise ValueError("The number of vertices must be a positive integer.")
g = DiGraph()
g.name("Path on "+str(n)+" vertices")
if n:
g.add_path(range(n))
g.set_pos({i:(i,0) for i in range(n)})
return g
def Path(self,n):
r"""
Returns a directed path on `n` vertices.
INPUT:
- ``n`` (integer) -- number of vertices in the path.
EXAMPLES::
sage: g = digraphs.Path(5)
sage: g.vertices()
[0, 1, 2, 3, 4]
sage: g.size()
4
sage: g.automorphism_group().cardinality()
1
"""
g = DiGraph(n)
g.name("Path")
if n:
g.add_path(range(n))
g.set_pos({i:(i,0) for i in range(n)})
return g
def Path(self, n):
r"""
Returns a directed path on `n` vertices.
INPUT:
- ``n`` (integer) -- number of vertices in the path.
EXAMPLES::
sage: g = digraphs.Path(5)
sage: g.vertices()
[0, 1, 2, 3, 4]
sage: g.size()
4
sage: g.automorphism_group().cardinality()
1
"""
if n < 0:
raise ValueError(
"The number of vertices must be a positive integer.")
g = DiGraph()
g.name("Path on " + str(n) + " vertices")
if n:
g.add_path(range(n))
g.set_pos({i: (i, 0) for i in range(n)})
return g
