EN|RU Volume 17, No 5, 2010, P. 46-55 UDC 519.174 E. V. Konstantinova, A. N. Medvedev Cycles of length seven in the pancake graph Abstract: It was proved that a cycle $C_l$ of length $l$, $6\leq l\leq n!$, can be embedded in the pancake graph $P_n$, $n\geq3$, that is the Cayley graph on the symmetric group with the generating set of all prefix-reversals. In this paper the characterization of cycles of length seven in this graph is given. It is proved that each of the vertices in $P_n$, $n\geq4$, belongs to $7(n-3)$ cycles of length seven, and there are exactly $n!(n-3)$ different cycles of length seven in the graph $P_n$, $n\geq4$. Ill. 1, tab. 1, bibliogr. 7. Keywords: the pancake graph, Cayley graph, the symmetric group, cycle embedding. Konstantinova Elena Valentinovna 1,2 Medvedev Alexey Nikolaevich 2 1. S. L. Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia 2. Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia e-mail: e_konsta@math.nsc.ru, an_medvedev@yahoo.com © Sobolev Institute of Mathematics, 2015