Spectrum of Cayley graphs on the symmetric group generated by transpositions

Roi Krakovski; Bojan Mohar

Spectrum of Cayley graphs on the symmetric group generated by transpositions

Combinatorics 2012-05-01 v2

Authors: Roi Krakovski , Bojan Mohar

Abstract

For an integer $n\geq 2$ , let $X_n$ be the Cayley graph on the symmetric group $S_n$ generated by the set of transpositions ${(1 2),(1 3),...,(1 n)}$ . It is shown that the spectrum of $X_n$ contains all integers from $-(n-1)$ to $n-1$ (except 0 if $n=2$ or $n=3$ ).

Keywords

cayley graphs symmetric group transpositions spectrum eigenvalues algebraic graph theory

Cite

@article{arxiv.1201.2167,
  title  = {Spectrum of Cayley graphs on the symmetric group generated by transpositions},
  author = {Roi Krakovski and Bojan Mohar},
  journal= {arXiv preprint arXiv:1201.2167},
  year   = {2012}
}

Comments

We have been informed by Guillaume Chapuy, Valentin F\'eray and Paul Renteln, that the problem in question can be solved by exploiting certain properties of the Jucys-Murphy elements, discovered by Jucys and independently by Flatto, Odlyzko and Wales

Spectrum of Cayley graphs on the symmetric group generated by transpositions

Abstract

Keywords

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