The Directed Graph CnX2Cm. The directed graph CnX2Cm is obtained form the Cartesian product CnXCm by taking a single m-cycle and joining vertex u to vertex v in this m-cycle if and only if the distance from u tp v is 2 in the original m-cycle. C7X2C5 is pictured abovewhere the m-cycle htat has been squared is on the bottom level.

We ask, when is CnX2Cm hamiltonian? We have been quite successful in deriving sufficient conditons for this a particular graph. However, this area of research is still open.

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