On the Genus of Pancake Network

Both the pancake graph and star graph are Cayley graphs and are especially attractive for parallel processing. They both ‎have sublogarithmic diameter, and are fairly sparse compared to hypercubes. In this paper, we focus on another important ‎property, namely the genus. The genus of a graph is the minimum number of handles needed for drawing the graph on the ‎plane without edges crossing. We will investigate the upper bound and lower bound for the genus of pancake graph and ‎compare these values with the genus of the star graph as well as that of the hypercube. ‎