On the generalization of the pancake network

In this study, we are particularly interested in one class of symmetric interconnection networks, namely the pancake graph, P_n . Pancake graphs are especially attractive for distributed processing because they compare favorably with a hypercube of similar size. They have smaller degree and diameter than correspondingly large hypercubes. The one-sided pancake graph, P_n, has been modeled as a Cayley graph on S_n, the symmetric group of order n, while the two-sided pancake graph, 2P_n, has been represented as a Cayley graph on the wreath product S₂S_n. In this paper, we want to generalize the pancake graph, i.e., state the m-sided pancake flipping problem, and describe its graph as the m-sided pancake graph, mP_n. Specifically, 1. we shall model the m-sided pancake graph, mP_n as Cayley graph on the wreath product of some finite groups; then, 2. we shall look into the degree, diameter and the routing protocol of the m-sided pancake graph, mP_n ; 3. we shall give the bounds for the diameters of mP_n; and, 4. we shall give the diameters of 3P_n for 1 ⩽ n ⩽ 6