def operate_on(self,G):
# Operate on a hairy graph by deleting an edge and adding a hair to one of the vertices adjacent to the
# deleted edge.
sgn0 = -1 if G.order() % 2 else 1
image=[]
for (i, e) in enumerate(G.edges(labels=False)):
(u, v) = e
# Only edges not connected to a hair-vertex can be cut
if u >= self.domain.n_vertices or v >= self.domain.n_vertices:
continue
G1 = copy(G)
if not self.domain.even_edges:
Shared.enumerate_edges(G1)
e_label = G1.edge_label(u, v)
G1.delete_edge((u, v))
new_hair_idx = self.domain.n_vertices + self.domain.n_hairs
G1.add_vertex(new_hair_idx)
G2 = copy(G1)
G1.add_edge((u, new_hair_idx))
G2.add_edge((v, new_hair_idx))
if not self.domain.even_edges:
G1.set_edge_label(u, new_hair_idx, e_label)
G2.set_edge_label(v, new_hair_idx, e_label)
sgn1 = Shared.edge_perm_sign(G1)
sgn2 = Shared.edge_perm_sign(G2)
else:
sgn1 = 1
sgn2 = -1
image.append((G1, sgn1*sgn0))
image.append((G2, sgn2*sgn0))
return image
def operate_on(self, G):
# Operate on a bi colored hairy graph by deleting an edge and adding a hair of colour a to one of the adjacent
# vertices and a hair of colour b to the other adjacent vertex.
sgn0 = -1 if G.order() % 2 else 1
image = []
for (i, e) in enumerate(G.edges(labels=False)):
(u, v) = e
# Only edges not connected to a hair-vertex can be split.
if u >= self.domain.n_vertices or v >= self.domain.n_vertices:
continue
G1 = copy(G)
if not self.domain.even_edges:
Shared.enumerate_edges(G1)
e_label = G1.edge_label(u, v)
G1.delete_edge((u, v))
new_hair_idx_1 = self.domain.n_vertices + self.domain.n_hairs
new_hair_idx_2 = new_hair_idx_1 + 1
G1.add_vertex(new_hair_idx_1)
G1.add_edge((u, new_hair_idx_1))
G1.add_vertex(new_hair_idx_2)
G1.add_edge((v, new_hair_idx_2))
G2 = copy(G1)
vertices = list(range(0, self.domain.n_vertices))
vertices = [] if vertices is None else vertices
start_idx_a = self.domain.n_vertices
start_idx_b = self.domain.n_vertices + self.domain.n_hairs_a + 1
hairs_a = list(range(start_idx_a + 1, start_idx_b))
hairs_a = [] if hairs_a is None else hairs_a
hairs_b = list(range(start_idx_b, new_hair_idx_2))
hairs_b = [] if hairs_b is None else hairs_b
p = vertices + hairs_a + hairs_b
p1 = p + [start_idx_a, new_hair_idx_2]
G1.relabel(p1)
p2 = p + [new_hair_idx_2, start_idx_a]
G2.relabel(p2)
if not self.domain.even_edges:
G1.set_edge_label(u, start_idx_a, e_label)
G1.set_edge_label(v, new_hair_idx_2, G1.size() - 1)
sgn1 = Shared.edge_perm_sign(G1)
G2.set_edge_label(v, start_idx_a, e_label)
G2.set_edge_label(u, new_hair_idx_2, G2.size() - 1)
sgn2 = Shared.edge_perm_sign(G2)
else:
sgn1 = 1
sgn2 = -1
image.append((G1, sgn1 * sgn0))
image.append((G2, sgn2 * sgn0))
return image
