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C_{n}X_{2}C_{m}

__The Directed Graph__ C_{n}X_{2}C_{m}.
The directed graph C_{n}X_{2}C_{m} is obtained
form the Cartesian product C_{n}XC_{m} 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. C_{7}X_{2}C_{5}
is pictured abovewhere the m-cycle htat has been squared is on the bottom
level.
We ask, when is C_{n}X_{2}C_{m} hamiltonian?
We have been quite successful in deriving sufficient conditons for this
a particular graph. However, this area of research is still open.

C_{7}X_{2}C_{5}
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