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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 205–213 (Mi semr911)  

Discrete mathematics and mathematical cybernetics

Greedy cycles in the star graphs

D. A. Gostevskya, E. V. Konstantinovabc

a St Petersburg Academic University, st. Khlopina, 8/3, 194021, St Petersburg, Russia
b Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
c Novosibirsk State University, st. Pirogova, 2, 630090, Novosibirsk, Russia

Abstract: We apply the greedy approach to construct greedy cycles in Star graphs $S_n, n\geqslant 3,$ defined as Cayley graphs on the symmetric group $\mathrm{Sym}_n$ with generating set $t=\{(1 i),2\leqslant i\leqslant n\}$ of transpositions. We define greedy sequences presented by distinct elements from $t$, and prove that any greedy sequence of length $k$, $2\leqslant k\leqslant n-1$, forms a greedy cycle of length $2\cdot3^{k-1}$. Based on these greedy sequences we give a construction of a maximal set of independent greedy cycles in the Star graphs $S_n$ for any $n\geqslant 3$.

Keywords: Cayley graph; Star graph; greedy sequence; greedy cycle.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-51-560008
18-01-00353
The reported study was funded by RFBR according to the research projects 17-51-560008 and 18-01-00353.


DOI: https://doi.org/10.17377/semi.2018.15.020

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Bibliographic databases:

Document Type: Article
UDC: 519.1
MSC: 05C25
Received October 10, 2017, published March 13, 2018
Language: English

Citation: D. A. Gostevsky, E. V. Konstantinova, “Greedy cycles in the star graphs”, Sib. Èlektron. Mat. Izv., 15 (2018), 205–213

Citation in format AMSBIB
\Bibitem{GosKon18}
\by D.~A.~Gostevsky, E.~V.~Konstantinova
\paper Greedy cycles in the star graphs
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 205--213
\mathnet{http://mi.mathnet.ru/semr911}
\crossref{https://doi.org/10.17377/semi.2018.15.020}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000438412200020}


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