Geodesic
Cycles of length seven in the pancake graph
Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 5, pp. 46-55.

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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. 
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E. V. Konstantinova; A. N. Medvedev. Cycles of length seven in the pancake graph. Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 5, pp. 46-55. http://geodesic.mathdoc.fr/item/DA_2010_17_5_a4/

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