Cartesian product of graphs

In graph theory, the Cartesian product G ${\displaystyle \square }$ H of graphs G and H is a graph such that

Cartesian product graphs can be recognized efficiently, in linear time. The operation is commutative as an operation on isomorphism classes of graphs, and more strongly the graphs G ${\displaystyle \square }$ H and H ${\displaystyle \square }$ G are naturally isomorphic, but it is not commutative as an operation on labeled graphs. The operation is also associative, as the graphs (F ${\displaystyle \square }$ G) ${\displaystyle \square }$ H and F ${\displaystyle \square }$ (G ${\displaystyle \square }$ H) are naturally isomorphic.

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