  This work deals with quantum graphs, focusing on the transmission properties
they engender. We first select two simple diamond graphs, and two hexagonal
graphs in which the vertices are all of degree 3, and investigate their
transmission coefficients. In particular, we identified regions in which the
transmission is fully suppressed. We also considered the transmission
coefficients of some series and parallel arrangements of the two basic graphs,
with the vertices still preserving the degree 3 condition, and then identified
specific series and parallel compositions that allow for windows of no
transmission. Inside some of these windows, we found very narrow peaks of full
transmission, which are consequences of constructive quantum interference.
Possibilities of practical use as the experimental construction of devices of
current interest to control and manipulate quantum transmission are also
discussed.
