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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2016, Volume 13, Pages 1258–1270
DOI: https://doi.org/10.17377/semi.2016.13.098
(Mi semr748)
 

This article is cited in 5 scientific papers (total in 6 papers)

Discrete mathematics and mathematical cybernetics

Multiplicities of eigenvalues of the Star graph

S. V. Avgustinovicha, E. N. Khomyakovab, E. V. Konstantinovaab

a Sobolev Institute of Mathematics, pr. Koptyuga 4, 630090, Novosibirsk, Russia
b Novosibisk State University, Pirogova, 2, 630090, Novosibirsk, Russia
Full-text PDF (492 kB) Citations (6)
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Abstract: The Star graph $S_n$, $n\geqslant 2$, is the Cayley graph on the symmetric group $\mathrm{Sym}_n$ generated by the set of transpositions [4] $\{(1~2), (1~3), \ldots, (1~n)\}$. We consider the spectrum of the Star graph as the spectrum of its adjacency matrix. It is known that the spectrum of $S_n$ is integral. Analytic formulas for multiplicities of eigenvalues $\pm(n-k)$ for $k = 2, 3, 4, 5$ in the Star graph are given in this paper. We also prove that any fixed integer has multiplicity at least $2^{\frac{1}{2}n \log n (1-o(1))}$ as an eigenvalue of $S_n$.
Keywords: Cayley graph, Star graph, symmetric group, graph spectrum, eigenvalues, multiplicity.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-05867_а
15-01-07906_а
Received September 28, 2016, published December 23, 2016
Bibliographic databases:
Document Type: Article
UDC: 519.1
Language: English
Citation: S. V. Avgustinovich, E. N. Khomyakova, E. V. Konstantinova, “Multiplicities of eigenvalues of the Star graph”, Sib. Èlektron. Mat. Izv., 13 (2016), 1258–1270
Citation in format AMSBIB
\Bibitem{AvgKhoKon16}
\by S.~V.~Avgustinovich, E.~N.~Khomyakova, E.~V.~Konstantinova
\paper Multiplicities of eigenvalues of the Star graph
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 1258--1270
\mathnet{http://mi.mathnet.ru/semr748}
\crossref{https://doi.org/10.17377/semi.2016.13.098}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000407781100098}
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  • https://www.mathnet.ru/eng/semr/v13/p1258
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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