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}});
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i2 : H = graph({3,4,5},{{3,4},{4,5}});
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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
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The object directProduct is a method function.