The Star graph eigenfunctions with non-zero eigenvalues

The Star graph eigenfunctions with non-zero eigenvalues Full article

Journal

Linear Algebra and Its Applications
ISSN: 0024-3795

Output data

Year: 2021, Volume: 610, Pages: 222-226 Pages count : 5 DOI: 10.1016/j.laa.2020.09.042

Tags

Eigenfunction; Eigenvalue; Star graph; Symmetric group

Authors

Kabanov V.V. ^1,2 , Konstantinova E.V. ^2,4 , Shalaginov L. ^1,2,3 , Valyuzhenich A. ^2,4

Affiliations

1	Krasovskii Institute of Mathematics and Mechanics, S. Kovalevskaja st. 16, Yekaterinburg, 620990, Russian Federation
2	Sobolev Institute of Mathematics, Ak. Koptyug av. 4, Novosibirsk, 630090, Russian Federation
3	Chelyabinsk State University, Brat'ev Kashirinyh st. 129, Chelyabinsk, 454021, Russian Federation
4	Novosibirsk State University, Pirogova str. 2, Novosibirsk, 630090, Russian Federation

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. © 2020 Elsevier Inc.

Kabanov V.V. , Konstantinova E.V. , Shalaginov L. , Valyuzhenich A.
The Star graph eigenfunctions with non-zero eigenvalues
Linear Algebra and Its Applications. 2021. V.610. P.222-226. DOI: 10.1016/j.laa.2020.09.042 WOS Scopus OpenAlex

Web of science:	WOS:000596321700012
Scopus:	2-s2.0-85092077395
OpenAlex:	W3090925795

DB	Citing
Scopus	2
OpenAlex	3
Web of science	2