The Star graph eigenfunctions with non-zero eigenvalues

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The Star graph eigenfunctions with non-zero eigenvalues. / Kabanov, Vladislav V.; Konstantinova, Elena V.; Shalaginov, Leonid et al.

In: Linear Algebra and Its Applications, Vol. 610, 01.02.2021, p. 222-226.

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

Harvard

Kabanov, VV, Konstantinova, EV, Shalaginov, L & Valyuzhenich, A 2021, 'The Star graph eigenfunctions with non-zero eigenvalues', Linear Algebra and Its Applications, vol. 610, pp. 222-226. https://doi.org/10.1016/j.laa.2020.09.042

APA

Kabanov, V. V., Konstantinova, E. V., Shalaginov, L., & Valyuzhenich, A. (2021). The Star graph eigenfunctions with non-zero eigenvalues. Linear Algebra and Its Applications, 610, 222-226. https://doi.org/10.1016/j.laa.2020.09.042

Vancouver

Kabanov VV, Konstantinova EV, Shalaginov L, Valyuzhenich A. The Star graph eigenfunctions with non-zero eigenvalues. Linear Algebra and Its Applications. 2021 Feb 1;610:222-226. doi: 10.1016/j.laa.2020.09.042

Author

Kabanov, Vladislav V. ; Konstantinova, Elena V. ; Shalaginov, Leonid et al. / The Star graph eigenfunctions with non-zero eigenvalues. In: Linear Algebra and Its Applications. 2021 ; Vol. 610. pp. 222-226.

BibTeX

@article{cb60d51c3a624026a0d1c862b5e58699,

title = "The Star graph eigenfunctions with non-zero eigenvalues",

abstract = "We consider the symmetric group SymΩ with Ω={1,…,n} for any integer n⩾2 and a set S={(1i),i∈{2,…,n}}. The Star graph Sn=Cay(SymΩ,S) is the Cayley graph over the symmetric group SymΩ with the generating set S. For n⩾3, the spectrum of the Star Sn is integral such that for each integer 1⩽k⩽n−1, the values ±(n−k) are its eigenvalues; if n⩾4, then 0 is also an eigenvalue of Sn. A family of PI-eigenfunctions of the Star graph Sn,n⩾3, has been obtained recently for eigenvalues [Formula presented]. We generalise the family of PI-eigenfunctions and present a family of eigenfunctions for all non-zero eigenvalues of this graph.",

keywords = "Eigenfunction, Eigenvalue, Star graph, Symmetric group",

author = "Kabanov, {Vladislav V.} and Konstantinova, {Elena V.} and Leonid Shalaginov and Alexandr Valyuzhenich",

year = "2021",

month = feb,

day = "1",

doi = "10.1016/j.laa.2020.09.042",

language = "English",

volume = "610",

pages = "222--226",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Science Inc.",

}

RIS

TY - JOUR

T1 - The Star graph eigenfunctions with non-zero eigenvalues

AU - Kabanov, Vladislav V.

AU - Konstantinova, Elena V.

AU - Shalaginov, Leonid

AU - Valyuzhenich, Alexandr

PY - 2021/2/1

Y1 - 2021/2/1

N2 - We consider the symmetric group SymΩ with Ω={1,…,n} for any integer n⩾2 and a set S={(1i),i∈{2,…,n}}. The Star graph Sn=Cay(SymΩ,S) is the Cayley graph over the symmetric group SymΩ with the generating set S. For n⩾3, the spectrum of the Star Sn is integral such that for each integer 1⩽k⩽n−1, the values ±(n−k) are its eigenvalues; if n⩾4, then 0 is also an eigenvalue of Sn. A family of PI-eigenfunctions of the Star graph Sn,n⩾3, has been obtained recently for eigenvalues [Formula presented]. We generalise the family of PI-eigenfunctions and present a family of eigenfunctions for all non-zero eigenvalues of this graph.

AB - We consider the symmetric group SymΩ with Ω={1,…,n} for any integer n⩾2 and a set S={(1i),i∈{2,…,n}}. The Star graph Sn=Cay(SymΩ,S) is the Cayley graph over the symmetric group SymΩ with the generating set S. For n⩾3, the spectrum of the Star Sn is integral such that for each integer 1⩽k⩽n−1, the values ±(n−k) are its eigenvalues; if n⩾4, then 0 is also an eigenvalue of Sn. A family of PI-eigenfunctions of the Star graph Sn,n⩾3, has been obtained recently for eigenvalues [Formula presented]. We generalise the family of PI-eigenfunctions and present a family of eigenfunctions for all non-zero eigenvalues of this graph.

KW - Eigenfunction

KW - Eigenvalue

KW - Star graph

KW - Symmetric group

UR - http://www.scopus.com/inward/record.url?scp=85092077395&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2020.09.042

DO - 10.1016/j.laa.2020.09.042

M3 - Article

AN - SCOPUS:85092077395

VL - 610

SP - 222

EP - 226

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

ID: 25676059