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 test_adjacent_vertices_of_star_is_not_independent_set():
G = gp.star_graph(3)
assert gp.is_independent_set(G, [0, 1]) is False
assert gp.is_independent_set(G, [0, 2]) is False
def test_connected_zero_forcing_number_of_monster_is_4(self):
G = gp.star_graph(3)
G.add_edge(3, 4)
G.add_edge(3, 5)
assert gp.connected_zero_forcing_number(G) == 4
def test_leaf_is_max_degree_minus_one_forcing_set_for_star(self):
for i in range(3, 13):
G = gp.star_graph(i)
D = gp.max_degree(G)
assert gp.is_k_forcing_set(G, [1], D - 1) == True
def test_non_integral_value_for_k_raises_TypeError_in_is_k_forcing(self):
with pytest.raises(TypeError):
G = gp.star_graph(2)
gp.is_k_forcing_vertex(G, 1, [1], 1.5)
def test_center_of_star_is_not_zero_forcing_active_set(self):
G = gp.star_graph(2)
assert gp.is_zero_forcing_active_set(G, [0]) == False
def test_center_of_S3_is_not_2_forcing_vertex(self):
G = gp.star_graph(3)
assert gp.is_k_forcing_vertex(G, 0, [0], 2) == False
def test_no_vertex_is_zero_forcing_vertex_for_empty_set(self):
G = gp.star_graph(2)
assert gp.is_zero_forcing_vertex(G, 0, set()) == False
assert gp.is_zero_forcing_vertex(G, 1, set()) == False
assert gp.is_zero_forcing_vertex(G, 2, set()) == False
def test_zero_value_for_k_raises_ValueError(self):
with pytest.raises(ValueError):
G = gp.star_graph(2)
gp.sub_k_domination_number(G, 0)
def test_matching_number_of_star_is_1():
for i in range(1, 11):
G = gp.star_graph(i)
assert gp.matching_number(G, method="bf") == 1
assert gp.matching_number(G, method="ilp") == 1
def test_min_maximal_matching_number_of_star_is_1():
for i in range(1, 11):
G = gp.star_graph(i)
assert gp.min_maximal_matching_number(G) == 1
def test_independence_number_of_star_is_order_minus_1():
for i in range(1, 10):
G = gp.star_graph(i)
assert gp.independence_number(G, method="bf") == G.order() - 1
assert gp.independence_number(G, method="ilp") == G.order() - 1
def test_center_and_two_leaves_of_star_is_not_2_independent_set():
G = gp.star_graph(3)
assert gp.is_independent_set(G, [0, 1, 2]) is False
def test_set_of_leaves_of_star_is_2_independent_set():
for i in range(2, 10):
G = gp.star_graph(i)
ind_set = set(j for j in range(1, i + 1))
assert gp.is_k_independent_set(G, ind_set, 2) is True
def test_leaf_is_zero_forcing_vertex_for_star(self):
G = gp.star_graph(2)
assert gp.is_zero_forcing_vertex(G, 1, [1]) == True
def test_integral_float_for_k_works(self):
G = gp.star_graph(2)
assert gp.sub_k_domination_number(G, 1.0) == 1
def test_center_is_not_zero_forcing_vertex_for_star(self):
G = gp.star_graph(2)
assert gp.is_zero_forcing_vertex(G, 0, [0]) == False
def test_non_integral_value_for_k_raises_TypeError(self):
with pytest.raises(TypeError):
G = gp.star_graph(2)
gp.sub_k_domination_number(G, 1.5)
def test_center_of_S3_is_3_forcing_vertex(self):
G = gp.star_graph(3)
assert gp.is_k_forcing_vertex(G, 0, [0], 3) == True
def test_annihilation_number_of_star_is_order_minus_1(self):
for i in range(2, 11):
G = gp.star_graph(i)
assert gp.annihilation_number(G) == G.order() - 1
def test_leaf_of_star_is_zero_forcing_active_set(self):
G = gp.star_graph(2)
assert gp.is_zero_forcing_active_set(G, [1]) == True
def test_0_value_for_k_raises_ValueError_in_is_k_forcing(self):
with pytest.raises(ValueError):
G = gp.star_graph(2)
gp.is_k_forcing_vertex(G, 1, [1], 0)
def test_empy_set_is_not_zero_forcing_active_set(self):
G = gp.star_graph(2)
assert gp.is_zero_forcing_active_set(G, set()) == False
def test_non_int_value_for_k_raises_error_in_connected_k_forcing_num(self):
with pytest.raises(TypeError):
G = gp.star_graph(2)
gp.connected_k_forcing_number(G, 1.5)
def test_leaf_is_not_zero_forcing_set_of_S3(self):
G = gp.star_graph(3)
assert gp.is_zero_forcing_set(G, [1]) == False
def test_0_value_for_k_raises_error_in_connected_k_forcing_num(self):
with pytest.raises(ValueError):
G = gp.star_graph(2)
gp.connected_k_forcing_number(G, 0)
def test_zero_forcing_number_of_star_is_order_minus_2(self):
for i in range(2, 12):
G = gp.star_graph(i)
assert gp.zero_forcing_number(G) == G.order() - 2
def test_integral_float_for_k_works(self):
G = gp.star_graph(2)
assert gp.is_k_forcing_vertex(G, 1, [1], 1.0) == True
def test_non_int_value_for_k_raises_error_in_is_connected_k_forcing(self):
with pytest.raises(TypeError):
G = gp.star_graph(2)
gp.is_connected_k_forcing_set(G, [0], 1.5)
def test_center_node_is_power_dominating_set_of_star(self):
for i in range(1, 11):
G = gp.star_graph(i)
assert gp.is_power_dominating_set(G, [0]) == True