On the genus of pancake network

الملخص EN

Both the pancake graph and star graph are Cayley graphs and are especially attractive for parallel processing.

They both have sub logarithmic diameter, and are fairly sparse compared to hypercube.

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.