The genus of the complete multipartite graph and the complete multi-layered graph

Abstract

The complete multipartite graph and the complete multi-layered graph are both generalizations of the complete bipartite graph. These two kinds of graphs have recursive structure and offer a very flexible choice of network size with respect to a fixed network order. This paper addresses the genus of the complete multipartite graph and the complete multi-layered graph which measures how efficiently we can set up a computer network using these graph layouts.