Catalogue of the Star graph eigenvalue multiplicities

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Abstract

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.

Original languageEnglish
Number of pages5
JournalArabian Journal of Mathematics
DOIs
Publication statusPublished - 29 Nov 2019

Keywords

  • CAYLEY-GRAPHS
  • SPECTRA

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