On the commutation graph of cyclic $TI$-subgroups in unitary groups

In this work the commutation graph $\Gamma(A)$ of a cyclic $TI$-subgroup $A$ of order 4 in a finite group $G$ with quasi-simple generalized Fitting subgroup $F^*(G)$ is investigated on subject of the symmetric property. We prove that, if $F^*(G)$ is a unitary group, then the graph $\Gamma(A)$ is either a coclique or an edge-regular but not coedge-regular graph.