def is_bull_free(G):
"""Returns True if *G* is bull-free, and False otherwise.
A graph is *bull-free* if it contains no induced subgraph isomorphic to the
bull graph, where the bull graph is the complete graph on 3 vertices with
two pendants added to two of its vertices.
Parameters
----------
G : NetworkX graph
An undirected graph.
Returns
-------
boolean
True if *G* is bull-free, false otherwise.
Examples
--------
>>> G = gp.complete_graph(4)
>>> gp.is_bull_free(G)
True
"""
# define a bull graph, also known as the graph obtained from the complete graph K_3 by addiing two pendants
bull = gp.Graph([(0, 1), (0, 2), (1, 2), (1, 3), (2, 4)])
# enumerate over all possible combinations of 5 vertices contained in G
for S in set(itertools.combinations(G.nodes(), 5)):
H = G.subgraph(list(S))
if gp.is_isomorphic(H, bull):
return False
# if the above loop completes, the graph is bull-free
return True
def is_claw_free(G):
"""Returns True if *G* is claw-free, and False otherwise.
A graph is *claw-free* if it contains no induce subgraph isomorphic to the
star on four vertices.
Parameters
----------
G : NetworkX graph
An undirected graph.
Returns
-------
boolean
True if *G* is claw-free, and False otherwise.
Examples
--------
>>> G = gp.complete_graph(4)
>>> gp.is_claw_free(G)
True
>>> G = gp.star_graph(4)
>> gp.is_claw_free(G)
False
"""
# define a claw graph, also known as the complete bipartite graph K_1,3
claw = gp.star_graph(3)
# enumerate over all possible combinations of 4 vertices contained in G
for S in set(itertools.combinations(G.nodes(), 4)):
H = G.subgraph(list(S))
if gp.is_isomorphic(H, claw):
return False
# if the above loop completes, the graph is claw-free
return True
def is_triangle_free(G):
"""Returns True if *G* is triangle-free, and False otherwise.
A graph is *triangle-free* if it contains no induced subgraph isomorphic to
the complete graph on 3 vertices.
Parameters
----------
G : NetworkX graph
An undirected graph.
Returns
-------
boolean
True if G is triangle-free, False otherwise.
Examples
--------
>>> G = gp.complete_graph(4)
>>> gp.is_triangle_free(G)
False
>>> G = gp.cycle_graph(5)
>> gp.is_triangle_free(G)
True
"""
# define a triangle graph, also known as the complete graph K_3
triangle = gp.complete_graph(3)
# enumerate over all possible combinations of 3 vertices contained in G
for S in set(itertools.combinations(G.nodes(), 3)):
H = G.subgraph(list(S))
if gp.is_isomorphic(H, triangle):
return False
# if the above loop completes, the graph is triangle free
return True
def graph_property_check(G, property):
if property == "is_planar":
return gp.check_planarity(G)[0]
elif property == "is_regular":
return gp.min_degree(G) == gp.max_degree(G)
elif property == "is_cubic":
return gp.min_degree(G) == 3 and gp.max_degree(G) == 3
elif property == "is_not_K_n":
return gp.is_isomorphic(G, gp.complete_graph(gp.number_of_nodes(G))) == False
elif property == "is_triangle_free":
return set(gp.triangles(G).values()) == {0}
else:
return getattr(gp, property)(G)