Sage Reference Manual: Graph Theory - Mirrors

Sage Reference Manual: Graph Theory, Release 6.1.1
EXAMPLES:
sage: G = graphs.CycleGraph(3)
sage: H = graphs.CycleGraph(4)
sage: J = G.disjoint_union(H); J
Cycle graph disjoint_union Cycle graph: Graph on 7 vertices
sage: J.vertices()
[(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (1, 3)]
sage: J = G.disjoint_union(H, verbose_relabel=False); J
Cycle graph disjoint_union Cycle graph: Graph on 7 vertices
sage: J.vertices()
[0, 1, 2, 3, 4, 5, 6]
sage: G=Graph({’a’: [’b’]})
sage: G.name("Custom path")
sage: G.name()
’Custom path’
sage: H=graphs.CycleGraph(3)
sage: J=G.disjoint_union(H); J
Custom path disjoint_union Cycle graph: Graph on 5 vertices
sage: J.vertices()
[(0, ’a’), (0, ’b’), (1, 0), (1, 1), (1, 2)]
disjunctive_product(other)
Returns the disjunctive product of self and other.
The disjunctive product of G and H is the graph L with vertex set V (L) = V (G) × V (H), and
((u, v), (w, x)) is an edge iff either :
•(u, w) is an edge of G, or
•(v, x) is an edge of H.
EXAMPLES:
sage: Z = graphs.CompleteGraph(2)
sage: D = Z.disjunctive_product(Z); D
Graph on 4 vertices
sage: D.plot() # long time
sage: C = graphs.CycleGraph(5)
sage: D = C.disjunctive_product(Z); D
Graph on 10 vertices
sage: D.plot() # long time
TESTS:
Disjunctive product of graphs:
sage: G = Graph([(0,1), (1,2)])
sage: H = Graph([(’a’,’b’)])
sage: T = G.disjunctive_product(H)
sage: T.edges(labels=None)
[((0, ’a’), (0, ’b’)), ((0, ’a’), (1, ’a’)), ((0, ’a’), (1, ’b’)), ((0, ’a’), (2, ’b’)), ((0
sage: T.is_isomorphic( H.disjunctive_product(G) )
True
Disjunctive product of digraphs:
sage: I = DiGraph([(0,1), (1,2)])
sage: J = DiGraph([(’a’,’b’)])
1.1. Generic graphs 43