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 setup_class(self):
G = gp.Graph()
G.add_edge(0, 1)
G.add_edge(0, 2)
G.add_edge(1, 2)
G.add_edge(0, 3)
G.add_edge(3, 4)
G.add_edge(3, 5)
self.G = G
def setup_class(self):
# The test graph for these functions is the simple graph obtained from
# the disjoint union of K_3 and P_3 by joining one vertex of K_3 with
# the degree two vertex of P_3.
G = gp.Graph()
G.add_edge(0, 1)
G.add_edge(0, 2)
G.add_edge(1, 2)
G.add_edge(0, 3)
G.add_edge(3, 4)
G.add_edge(3, 5)
self.G = G
def test_min_conn_dominating_for_disconnected_graph_is_0():
G = gp.Graph()
G.add_edge(1, 2)
G.add_edge(3, 4)
assert gp.connected_domination_number(G) == 0