We investigate the effects on the electronic structure induced by a relaxation of the graphite lattice along the direction of the phonons associated to the G and to the D peak characteristic of the Raman spectra of graphitic materials. To this aim the bond length dependence of the hopping integral beta is introduced in a Huckel (tight-binding) hamiltonian, giving rise to two different beta(1) and beta(2) parameters. A Peierls-like gap opening is found for a relaxation along the D peak phonon and not for the G peak phonon. The electronic density of states is discussed and a link is shown between the electronic structure of benzene and the electronic structure of graphene at the K point in reciprocal space. (c) 2005 Elsevier B.V. All rights reserved.