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Sib. Èlektron. Mat. Izv., 2014, Volume 11, Pages 906–914
(Mi semr535)
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This article is cited in 2 scientific papers (total in 2 papers)
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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UDC:
519.1
MSC: 05C25 Received October 15, 2014, published December 3, 2014
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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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http://mi.mathnet.ru/eng/semr535 http://mi.mathnet.ru/eng/semr/v11/p906
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This publication is cited in the following articles:
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Alexey N. Medvedev, “The number of small cycles in the Star graph”, Sib. elektron. matem. izv., 13 (2016), 286–299
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D. A. Gostevsky, E. V. Konstantinova, “Greedy cycles in the star graphs”, Sib. elektron. matem. izv., 15 (2018), 205–213
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