TY - JOUR

T1 - Catalogue of the Star graph eigenvalue multiplicities

AU - Khomyakova, Ekaterina

AU - Konstantinova, Elena V.

N1 - Publisher Copyright: © 2019, The Author(s).

PY - 2021/4

Y1 - 2021/4

N2 - 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.

AB - 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.

KW - CAYLEY-GRAPHS

KW - SPECTRA

UR - http://www.scopus.com/inward/record.url?scp=85075474882&partnerID=8YFLogxK

U2 - 10.1007/s40065-019-00271-z

DO - 10.1007/s40065-019-00271-z

M3 - Article

AN - SCOPUS:85075474882

VL - 10

SP - 115

EP - 119

JO - Arabian Journal of Mathematics

JF - Arabian Journal of Mathematics

SN - 2193-5343

IS - 1

ER -