In general, a graph product of two graphs G and H is a new graph whose vertex set is V(G)×V(H) and where, for any two vertices (g, h) and (g', h') in the product, the adjacency of those two vertices is determined entirely by the adjacency (or equality, or non-adjacency) of g and g', and that of h and h'. There are 3×3 - 1 = 8 cases to be decided (three possibilities for each, with the case where both are equal eliminated) and thus there are 2^8 = 256 different types of graph products that can be defined.
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