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Sib. Èlektron. Mat. Izv., 2014, Volume 11, Pages 906–914 (Mi semr535)  

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

Discrete mathematics and mathematical cybernetics

Small cycles in the star graph

Elena V. Konstantinovaab, Alexey N. Medvedevac

a Sobolev Institute of Mathematics, 4, Koptyug av., 630090, Novosibirsk, Russia
b Novosibisk State University, 2, Pirogova st., 630090, Novosibirsk, Russia
c Central European University, Nador ut. 9, Budapest, 1051, Hungary

Abstract: The Star graph is the Cayley graph on the symmetric group $Sym_n$ generated by the set of transpositions $\{(1 2),(1 3),\ldots,(1 n)\}$. These graphs are bipartite, they do not contain odd cycles but contain all even cycles with a sole exception $4$-cycles. We characterize all distinct $6$- and $8$-cycles by their canonical forms as products of generating elements. The number of these cycles in the Star graph is also given.

Keywords: Cayley graphs; Star graph; cycle embedding; product of generating elements.

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Document Type: Article
UDC: 519.1
MSC: 05C25
Received October 15, 2014, published December 3, 2014
Language: English

Citation: Elena V. Konstantinova, Alexey N. Medvedev, “Small cycles in the star graph”, Sib. Èlektron. Mat. Izv., 11 (2014), 906–914

Citation in format AMSBIB
\Bibitem{KonMed14}
\by Elena~V.~Konstantinova, Alexey~N.~Medvedev
\paper Small cycles in the star graph
\jour Sib. \`Elektron. Mat. Izv.
\yr 2014
\vol 11
\pages 906--914
\mathnet{http://mi.mathnet.ru/semr535}


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    Citing articles on Google Scholar: Russian citations, English citations
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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
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