Imbeddings of the tensor product of graphs where the second factor is a complete graph

Ghidewon Abay Asmerom
1998 Discrete Mathematics  
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 voltage
more » ... H* will be the desired tensor product of H with K". The genus of H ® K." where H is a graph with a quadrilateral imbedding and also H is either, bipartite, with bichromatic dual, or with straight-ahead imbedding is given *
doi:10.1016/s0012-365x(97)00130-1 fatcat:qqjsgziwo5eyblhlwtkhpoxvza