Catalogue of the Star graph eigenvalue multiplicities

Catalogue of the Star graph eigenvalue multiplicities Full article

Journal

Arabian Journal of Mathematics
ISSN: 2193-5343 , E-ISSN: 2193-5351

Output data

Year: 2021, Volume: 10, Number: 1, Pages: 115-119 Pages count : 5 DOI: 10.1007/s40065-019-00271-z

Authors

Khomyakova E. ¹ , Konstantinova E.V. ^1,2

Affiliations

1	Novosibirsk State University, Pirogova str. 2, Novosibirsk, 630090, Russian Federation
2	Sobolev Institute of Mathematics, Ak. Koptyug av. 4, Novosibirsk, 630090, Russian Federation

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. © 2019, The Author(s).

Khomyakova E. , Konstantinova E.V.
Catalogue of the Star graph eigenvalue multiplicities
Arabian Journal of Mathematics. 2021. V.10. N1. P.115-119. DOI: 10.1007/s40065-019-00271-z WOS Scopus OpenAlex

Web of science:	WOS:000499427100001
Scopus:	2-s2.0-85075474882
OpenAlex:	W2990716729

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