Trees associated to rational singularities

In this work, we define rational trees. Using the plumbing construction, th ese are just the dual resolution graphs of rational surface singularities. We prove that the number of rupture vertices of a rational tree A, which pr ovides a topological information on the singularity, is at most m - 2 for m greater than or equal to 3 where m is the multiplicity of the singularity whose dual graph of the minimal resolution is A. (C) 1999 Academie des scie nces/Editions scientifiques et medicales Elsevier SAS.