Sage Reference Manual: Graph Theory - Mirrors

Sage Reference Manual: Graph Theory, Release 6.1.1
sage: P = DiGraph([(0,1)])
sage: B = digraphs.DeBruijn( [’a’,’b’], 2 )
sage: Q = P.cartesian_product(B)
sage: Q.edges(labels=None)
[((0, ’aa’), (0, ’aa’)), ((0, ’aa’), (0, ’ab’)), ((0, ’aa’), (1, ’aa’)), ((0, ’ab’), (0, ’ba
sage: Q.strongly_connected_components_digraph().num_verts()
2
sage: V = Q.strongly_connected_component_containing_vertex( (0, ’aa’) )
sage: B.is_isomorphic( Q.subgraph(V) )
True
categorical_product(other)
Returns the tensor product of self and other.
The tensor product of G and H is the graph L with vertex set V (L) equal to the Cartesian product of the
vertices V (G) and V (H), and ((u, v), (w, x)) is an edge iff - (u, w) is an edge of self, and - (v, x) is an
edge of other.
The tensor product is also known as the categorical product and the kronecker product (refering to the
kronecker matrix product). See Wikipedia article on the Kronecker product.
EXAMPLES:
sage: Z = graphs.CompleteGraph(2)
sage: C = graphs.CycleGraph(5)
sage: T = C.tensor_product(Z); T
Graph on 10 vertices
sage: T.size()
10
sage: T.plot() # long time
sage: D = graphs.DodecahedralGraph()
sage: P = graphs.PetersenGraph()
sage: T = D.tensor_product(P); T
Graph on 200 vertices
sage: T.size()
900
sage: T.plot() # long time
TESTS:
Tensor product of graphs:
sage: G = Graph([(0,1), (1,2)])
sage: H = Graph([(’a’,’b’)])
sage: T = G.tensor_product(H)
sage: T.edges(labels=None)
[((0, ’a’), (1, ’b’)), ((0, ’b’), (1, ’a’)), ((1, ’a’), (2, ’b’)), ((1, ’b’), (2, ’a’))]
sage: T.is_isomorphic( H.tensor_product(G) )
True
Tensor product of digraphs:
sage: I = DiGraph([(0,1), (1,2)])
sage: J = DiGraph([(’a’,’b’)])
sage: T = I.tensor_product(J)
sage: T.edges(labels=None)
[((0, ’a’), (1, ’b’)), ((1, ’a’), (2, ’b’))]
sage: T.is_isomorphic( J.tensor_product(I) )
True
1.1. Generic graphs 23