  We examine scale invariant Fulop-Tsutsui couplings in a quantum vertex of a
general degree $n$. We demonstrate that essentially same scattering amplitudes
as for the free coupling can be achieved for two $(n-1)$-parameter
Fulop-Tsutsui subfamilies if $n$ is odd, and for three $(n-1)$-parameter
Fulop-Tsutsui subfamilies if $n$ is even. We also work up an approximation
scheme for a general Fulop-Tsutsui vertex, using only $n$ $\delta$ function
potentials.
