This article is cited in 9 papers

Cycles of length seven in the pancake graph

E. V. Konstantinova^ab, A. N. Medvedev<sup>b

a</sup> S. L. Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

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.

UDC: 519.174

Received: 03.02.2010
Revised: 01.04.2010

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