Macaulay2 » Documentation
Packages » Graphs :: strongProduct
next | previous | forward | backward | up | index | toc

strongProduct -- a method for taking the strong product of two graphs

Description

This method will take in any two graphs and output the strong product of the two graphs. The vertex set of the strong product of G and H is the cartesian product of the vertex sets of G and H. The keys for each vertex will be output as a sequence to represent this clearly. The edge set of the strong product of G and H is formed by the rule any two distinct vertices (u,u') and (v,v') are adjacent in G and H if and only if u' is adjacent with v' or u'=v' , and u is adjacent with v or u = v.

i1 : G = graph({1,2},{{1,2}});
 
i2 : H = graph({3,4,5},{{3,4},{4,5}});
 
i3 : strongProduct(G,H)

o3 = Graph{{1, 3} => {{2, 3}, {1, 4}, {2, 4}}                }
           {1, 4} => {{2, 5}, {1, 3}, {2, 3}, {2, 4}, {1, 5}}
           {1, 5} => {{2, 5}, {1, 4}, {2, 4}}
           {2, 3} => {{1, 3}, {1, 4}, {2, 4}}
           {2, 4} => {{2, 5}, {1, 3}, {2, 3}, {1, 4}, {1, 5}}
           {2, 5} => {{1, 4}, {2, 4}, {1, 5}}

o3 : Graph

See also

Ways to use strongProduct:

  • strongProduct(Graph,Graph)

For the programmer

The object strongProduct is a method function.

The source of this document is in Graphs.m2:4923:0.