The Pancake graph is well known because of the open Pancake problem. It has the structure that any l-cycle, 6 ≤ l ≤ n!, can be embedded in the Pancake graph Pn; n ≥ 3. Recently it was shown that there are exactly n! 6 independent 6-cycles and n!(n-3) distinct 7-cycles in the graph. In this paper we characterize all distinct 8-cycles by giving their canonical forms as products of generating elements. It is shown that there are exactly n!(n 3+12n2103n+176) 16 distinct 8-cycles in Pn; n ≥ 4. A maximal set of independent 8- cycles contains n! 8 of these.
|Number of pages||10|
|Journal||Ars Mathematica Contemporanea|
|Publication status||Published - 17 Jan 2014|
- Cayley graphs
- Cycle embedding
- Pancake graph
- Small cycles