  We study the spectrum of some periodic differential operators, in particular
the periodic Schr\"{o}dinger operator acting on infinite $n$-cubic graphs.
Using Floquet-Bloch theory, we derive and analyze on the dispersion relations
of the periodic quantum graph generated by 2-dimensional rectangles, and also
$n$-cubes. Our proof is analytic. These dispersion relations define the spectra
of the associated periodic operator, thus facilitating further analysis of the
spectra.
