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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{DA_2010_17_5_a4,
     author = {E. V. Konstantinova and A. N. Medvedev},
     title = {Cycles of length seven in the pancake graph},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {46--55},
     publisher = {mathdoc},
     volume = {17},
     number = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2010_17_5_a4/}
}
TY  - JOUR
AU  - E. V. Konstantinova
AU  - A. N. Medvedev
TI  - Cycles of length seven in the pancake graph
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2010
SP  - 46
EP  - 55
VL  - 17
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2010_17_5_a4/
LA  - ru
ID  - DA_2010_17_5_a4
ER  - 
%0 Journal Article
%A E. V. Konstantinova
%A A. N. Medvedev
%T Cycles of length seven in the pancake graph
%J Diskretnyj analiz i issledovanie operacij
%D 2010
%P 46-55
%V 17
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2010_17_5_a4/
%G ru
%F DA_2010_17_5_a4
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/