C_nX₂C_m

The Directed Graph C_nX₂C_m. The directed graph C_nX₂C_m is obtained form the Cartesian product C_nXC_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. C₇X₂C₅ is pictured abovewhere the m-cycle htat has been squared is on the bottom level.

We ask, when is C_nX₂C_m hamiltonian? We have been quite successful in deriving sufficient conditons for this a particular graph. However, this area of research is still open.

C₇X₂C₅ Return to previous page

CnX2Cm

C_nX₂C_m