Cayley Graph on Symmetric Group Generated by Elements Fixing $k$ Points

Kok Bin Wong, Terry Lau, Cheng Yeaw Ku

Let ${\mathcal{S}}_n$ be the symmetric group on $[n]=\{1,\dots ,n\}$. The $k$-point fixing graph $\mathcal{F}(n,k)$ is defined to be the graph with vertex set ${\mathcal{S}}_n$ a…