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Diskretn. Anal. Issled. Oper., 2011, Volume 18, Number 6, Pages 33–60 (Mi da669)  

This article is cited in 1 scientific paper (total in 1 paper)

Cycles of lentgth 9 in the Pancake graph

E. V. Konstantinovaab, A. N. Medvedeva

a Novosibirsk State University, Novosibirsk, Russia
b S. L. Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia

Abstract: A cycle $C_l$ of length $l$, where $6\le l\le n!$, can be embedded in the Pancake graph $P_n$, $n\ge3$, that is the Cayley graph on the symmetric group with the generating set of all prefix-reversals. The algebraic characterization of cycles of length six and seven via products of generating elements is known. We continue to study odd cycles. The explicit description of cycles of length nine by means of 10 canonical forms is given. It is also proved that each of vertices of $P_n$, $n\ge4,$ belongs to $\frac{8n^3-45n^2+61n-12}2$ cycles of length nine. In general, there are $O(n! n^3)$ different cycles of length nine in the graph. Ill. 5, tab. 1, bibliogr. 10.

Keywords: admissible subgraph, indicator of subgraph's quality, Pareto optimal subgraph.

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Bibliographic databases:

Document Type: Article
UDC: 519.174
Received: 25.04.2011
Revised: 13.07.2011

Citation: E. V. Konstantinova, A. N. Medvedev, “Cycles of lentgth 9 in the Pancake graph”, Diskretn. Anal. Issled. Oper., 18:6 (2011), 33–60

Citation in format AMSBIB
\Bibitem{KonMed11}
\by E.~V.~Konstantinova, A.~N.~Medvedev
\paper Cycles of lentgth~9 in the Pancake graph
\jour Diskretn. Anal. Issled. Oper.
\yr 2011
\vol 18
\issue 6
\pages 33--60
\mathnet{http://mi.mathnet.ru/da669}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2953799}
\zmath{https://zbmath.org/?q=an:1249.05208}


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    This publication is cited in the following articles:
    1. Alexey N. Medvedev, “The number of small cycles in the Star graph”, Sib. elektron. matem. izv., 13 (2016), 286–299  mathnet  crossref
  • Дискретный анализ и исследование операций
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