The phonon dispersion relation of the graphene comprises three acoustic (A) branches and three optical (O) branches. The modes are associated with out-of-plane (Z), in-plane longitudinal (L), and in-plane transverse (T) atomic motions (Fig. 2.10-a).
Figure 2.10-b shows the phonon dispersion branches of graphene. The three phonon dispersion branches, which originate from the -point of the BRILLOUIN zone correspond to acoustic modes: an out-of plane mode (ZA), an in-plane transverse mode (TA), and in-plane longitudinal (LA), listed in order of increasing energy. The remaining three branches correspond to optical modes: one out-of plane mode (ZO), and two in-plane modes (TO) and (LO).
While the TA and LA modes display the normal linear dispersion around the -point, the ZA mode shows a energy dispersion which is explained in  as a consequence of the point-group symmetry of graphene. Another consequence of the symmetry are the linear crossings of the ZA/ZO and the LA/LO modes at the -point.