On the genus of the tensor product of graphs where one factor is a regular graph

Tamara Dakić, Tomaž Pisanski
1994 Discrete Mathematics  
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
more » ... 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.
doi:10.1016/0012-365x(93)e0057-b fatcat:7ehxteqeanayxex6q5jinfa3am