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In this paper we present genus result for the tensor product of graphs where the second factor is the complete graph Km and m is a power of 2. We are going to view the second factor as a Cayley graph and we will use an imbedding technique that combines surgery and voltage graph theory. In this imbedding technique we start with a suitable imbedding of H on some surface and then modify the edges of H according to the nature of K., to get a voltage graph H*. The covering graph of this voltagedoi:10.1016/s0012-365x(97)00130-1 fatcat:qqjsgziwo5eyblhlwtkhpoxvza