Catalogue of the Star graph eigenvalue multiplicities

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Catalogue of the Star graph eigenvalue multiplicities. / Khomyakova, Ekaterina; Konstantinova, Elena V.

In: Arabian Journal of Mathematics, Vol. 10, No. 1, 04.2021, p. 115-119.

Research output: Contribution to journal › Article › peer-review

Harvard

Khomyakova, E & Konstantinova, EV 2021, 'Catalogue of the Star graph eigenvalue multiplicities', Arabian Journal of Mathematics, vol. 10, no. 1, pp. 115-119. https://doi.org/10.1007/s40065-019-00271-z

APA

Khomyakova, E., & Konstantinova, E. V. (2021). Catalogue of the Star graph eigenvalue multiplicities. Arabian Journal of Mathematics, 10(1), 115-119. https://doi.org/10.1007/s40065-019-00271-z

Vancouver

Khomyakova E, Konstantinova EV. Catalogue of the Star graph eigenvalue multiplicities. Arabian Journal of Mathematics. 2021 Apr;10(1):115-119. doi: 10.1007/s40065-019-00271-z

Author

Khomyakova, Ekaterina ; Konstantinova, Elena V. / Catalogue of the Star graph eigenvalue multiplicities. In: Arabian Journal of Mathematics. 2021 ; Vol. 10, No. 1. pp. 115-119.

BibTeX

@article{5639015043334d55a89efdc0fe1f7bd6,

title = "Catalogue of the Star graph eigenvalue multiplicities",

abstract = "The Star graph Sn, n⩾ 2 , is the Cayley graph over the symmetric group Sym n generated by transpositions (1i),2⩽i⩽n. This set of transpositions plays an important role in the representation theory of the symmetric group. The spectrum of Sn contains all integers from - (n- 1) to n- 1 , and also zero for n⩾ 4. In this paper we observe methods for getting explicit formulas of eigenvalue multiplicities in the Star graphs Sn, present such formulas for the eigenvalues ± (n- k) , where 2 ⩽ k⩽ 12 , and finally collect computational results of all eigenvalue multiplicities for n⩽ 50 in the catalogue.",

keywords = "CAYLEY-GRAPHS, SPECTRA",

author = "Ekaterina Khomyakova and Konstantinova, {Elena V.}",

note = "Publisher Copyright: {\textcopyright} 2019, The Author(s).",

year = "2021",

month = apr,

doi = "10.1007/s40065-019-00271-z",

language = "English",

volume = "10",

pages = "115--119",

journal = "Arabian Journal of Mathematics",

issn = "2193-5343",

publisher = "Springer Heidelberg",

number = "1",

}

RIS

TY - JOUR

T1 - Catalogue of the Star graph eigenvalue multiplicities

AU - Khomyakova, Ekaterina

AU - Konstantinova, Elena V.

PY - 2021/4

Y1 - 2021/4

N2 - The Star graph Sn, n⩾ 2 , is the Cayley graph over the symmetric group Sym n generated by transpositions (1i),2⩽i⩽n. This set of transpositions plays an important role in the representation theory of the symmetric group. The spectrum of Sn contains all integers from - (n- 1) to n- 1 , and also zero for n⩾ 4. In this paper we observe methods for getting explicit formulas of eigenvalue multiplicities in the Star graphs Sn, present such formulas for the eigenvalues ± (n- k) , where 2 ⩽ k⩽ 12 , and finally collect computational results of all eigenvalue multiplicities for n⩽ 50 in the catalogue.

AB - The Star graph Sn, n⩾ 2 , is the Cayley graph over the symmetric group Sym n generated by transpositions (1i),2⩽i⩽n. This set of transpositions plays an important role in the representation theory of the symmetric group. The spectrum of Sn contains all integers from - (n- 1) to n- 1 , and also zero for n⩾ 4. In this paper we observe methods for getting explicit formulas of eigenvalue multiplicities in the Star graphs Sn, present such formulas for the eigenvalues ± (n- k) , where 2 ⩽ k⩽ 12 , and finally collect computational results of all eigenvalue multiplicities for n⩽ 50 in the catalogue.

KW - CAYLEY-GRAPHS

KW - SPECTRA

UR - http://www.scopus.com/inward/record.url?scp=85075474882&partnerID=8YFLogxK

U2 - 10.1007/s40065-019-00271-z

DO - 10.1007/s40065-019-00271-z

M3 - Article

AN - SCOPUS:85075474882

VL - 10

SP - 115

EP - 119

JO - Arabian Journal of Mathematics

JF - Arabian Journal of Mathematics

SN - 2193-5343

IS - 1

ER -

ID: 22404582