  In this paper we aim at proving well-posedness of solutions obtained as
vanishing viscosity limits for the Cauchy problem on a traffic junction where
$m$ incoming and $n$ outgoing roads meet. The traffic on each road is governed
by a scalar conservation law $ \rho_{h,t} + f_h(\rho_h)_x = 0$, for $h\in
\{1,\ldots, m+n\}$. Our proof relies upon the complete description of the set
of road-wise constant solutions and its properties, which is of some interest
on its own. Then we introduce a family of Kruzhkov-type adapted entropies at
the junction and state a definition of admissible solution in the same spirit
as in \cite{diehl, ColomboGoatinConstraint, scontrainte, AC_transmission,
germes}.
