This method will take in any two graphs and output the strong proudct 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}});
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i2 : H = graph({3,4,5},{{3,4},{4,5}});
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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
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The object strongProduct is a method function.