The tensor product HOG where G is a 2k-regular graph can be regarded as a covering space of the permutation voltage graph H czk) obtained from H. Assuming that H is suitably imbedded in some orientable surface by modifying the edges of H according to the configuration of G we get the permutation voltage graph H c2') whose permutation derived graph is exactly HOG. This construction can also be extended to the tensor product HOG where G is a (2k+ 1)-regular graph with l-factor. Here we put the

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... ficient conditions on H and G so that the permutation derived imbedding obtained in this way is a minimal imbedding. We also give sample results -the genus of the tensor products H@K"", and H@Q, are calculated for certain graphs H.