Spectrum of Cayley graphs on the symmetric group generated by transpositions

Details Spectrum of Cayley graphs on the symmetric group generated by transpositions Spectrum of Cayley graphs on the symmetric group generated by transpositions

2012-01-10

arxiv.org/abs/1201.2167v1

Mathematics

Combinatorics

Scientific paper

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 $n=3$).

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