The girths of the cubic Pancake graphs

Abstract

The Pancake graphs P n , n 2, are Cayley graphs over the symmetric group Sym n generated by prefix-reversals. There are six generating sets of prefixreversals of cardinality three which give connected Cayley graphs over the symmetric group known as cubic Pancake graphs. In this paper we study the girth of the cubic Pancake graphs. It is proved that considered cubic Pancake graphs have the girths at most twelve.