The Star graph eigenfunctions with non-zero eigenvalues
| Autor: | Elena V. Konstantinova, Alexandr Valyuzhenich, Leonid Shalaginov, Vladislav V. Kabanov |
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| Rok vydání: | 2021 |
| Předmět: |
Numerical Analysis
Algebra and Number Theory Cayley graph 010102 general mathematics 010103 numerical & computational mathematics Mathematics::Spectral Theory Star (graph theory) Eigenfunction 01 natural sciences Graph Combinatorics Symmetric group Generating set of a group Discrete Mathematics and Combinatorics Geometry and Topology 0101 mathematics Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Linear Algebra and its Applications. 610:222-226 |
| ISSN: | 0024-3795 |
| Popis: | We consider the symmetric group Sym Ω with Ω = { 1 , … , n } for any integer n ⩾ 2 and a set S = { ( 1 i ) , i ∈ { 2 , … , n } } . The Star graph S n = Cay ( Sym Ω , S ) is the Cayley graph over the symmetric group Sym Ω with the generating set S. For n ⩾ 3 , the spectrum of the Star S n 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 S n . A family of PI-eigenfunctions of the Star graph S n , n ⩾ 3 , has been obtained recently for eigenvalues n − 2 , … , n − ⌊ n 2 ⌋ − 1 . We generalise the family of PI-eigenfunctions and present a family of eigenfunctions for all non-zero eigenvalues of this graph. |
| Databáze: | OpenAIRE |
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