Abstract: Applications of the operator extension theory to the spectral problems for the quantum graphs are based on the relations between the spectrum of a self-adjoint operator defined via the Krein resolvent formula and the spectrum of the corresponding Krein Q-function. The results obtained up to now in this context requires some rather restrictive conditions on the auxiliary symmetric operator which defines the Hamiltonian of the quantum graph as a self-adjoint extension; these conditions are never obeyed in interesting cases. We show that at least for the equilateral quantum graphs these conditions can be omitted and the problem of the description of the spectrum is completely reduced to the spectral analysis for the corresponding tight-binding Hamiltonians. The result are obtained jointly with J.Bruening and K.Pankrashkin.