The second largest eigenvalue of normal Cayley graphs on symmetric groups generated by cycles

Yuxuan Li, Binzhou Xia, Sanming Zhou

We study the normal Cayley graphs $\mathrm{Cay}(S_n,C(n,I))$ on the symmetric group $S_n$, where $I\subseteq \{2,3,\dots ,n\}$ and $C(n,I)$ is the set of all cycles in $S_n$ with…