О графе коммутирования $TI$-подгрупп в симметрических группах

We study the commutation graph $\Gamma _G(A)$ of cyclic $TI$-subgroup A of order 4 in a finite group $G$ with quasisimple generalized Fitting subgroup $F^*(G)$. It is proved that, if $F^*(G)$ is a covering group for $A_n$, then the graph $\Gamma _G(A)$ is edge-regular but not coedge-regular graph.