  Within the earlier developed high-energy-$\vec k\cdot \vec p$-Hamiltonian
approach to describe graphene-like materials the simulations of non-Abelian Zak
phases and band structure of the quasi-relativistic graphene model with a
flavors number $N=3$ have been performed in approximations with %of zero- and
non-zero values of and without gauge fields (flavors). It has been shown that a
Zak-phases set for non-Abelian Majorana-like excitations (modes) in Dirac
valleys of the quasirelativistic graphene model is the cyclic group
$\mathbf{Z}_{12}$. This group is deformed into $\mathbf{Z}_8$ at sufficiently
high momenta due to deconfinement of the modes. Since the deconfinement removes
the degeneracy of the eightfolding valleys, Weyl nodes and antinodes emerge. We
offer that a Majorana-like mass term of the quasirelativistic model effects on
the graphene band structure in a following way. Firstly the inverse symmetry
emerges at "switching on"\ of the mass term, and secondly the mass term shifts
the location of Weyl nodes and antinodes into the region of higher energies and
accordingly the Majorana-like modes can exist without mixing with the nodes.
