The Star graph eigenfunctions with non-zero eigenvalues

Vladislav V. Kabanov, Elena V. Konstantinova, Leonid Shalaginov, Alexandr Valyuzhenich

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)222-226
Number of pages5
JournalLinear Algebra and Its Applications
Volume610
DOIs
Publication statusPublished - 1 Feb 2021

Keywords

  • Eigenfunction
  • Eigenvalue
  • Star graph
  • Symmetric group

OECD FOS+WOS

  • 1.01 MATHEMATICS
  • 1.01.PN MATHEMATICS, APPLIED

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