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

directProduct -- Computes the direct product of two graphs

Synopsis

Description

This method will take in any two graphs and output the direct product of these two graphs. The vertex set of the direct product of G and H is the cartesian product of G and H's vertex sets. The keys for each vertex will be output as a sequence to represent this. Any two vertices (u,u') and (v,v') form an edge in the direct product of G and G if and only if u' is adjacent with v' and u is adjacent with v in the original graphs.

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

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

o3 : Graph

See also

Ways to use directProduct :

For the programmer

The object directProduct is a method function.