**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.