  Let $G$ be an Eulerian directed graph with an arc-labeling such that arcs
going out from the same vertex have different labels. In this work, we present
an algorithm to construct the Eulerian trail starting at an arbitrary vertex
$v$ of minimum lexicographical label among labels of all Eulerian trails
starting at this vertex.
  We also show an application of this algorithm to construct the minimal de
Bruijn sequence of a language.
