  Given a (directed) graph G=(V,A), a subset X of V is an interval of G
provided that for any a, b\in X and x\in V-X, (a,x)\in A if and only if
(b,x)\in A and (x,a)\in A if and only if (x,b)\in A. For example, \emptyset,
\{x\} (x \in V) and V are intervals of G, called trivial intervals. A graph,
all the intervals of which are trivial, is indecomposable; otherwise, it is
decomposable. A vertex x of an indecomposable graph is critical if G-x is
decomposable. In 1993, J.H. Schmerl and W.T. Trotter characterized the
indecomposable graphs, all the vertices of which are critical, called critical
graphs. In this article, we characterize the indecomposable graphs which admit
a single non critical vertex, that we call (-1)-critical graphs.} This gives an
answer to a question asked by Y. Boudabbous and P. Ille in a recent article
studying the critical vertices in an indecomposable graph.
