The graph isomorphism problem consists in deciding if two given graphs have an identical structure. This problem can be modeled as a constraint satisfaction problem in a very straightforward way, so that one can use constraint programming to solve it. However, constraint programming is a generic tool that may be less efficient than dedicated algorithms which can take advantage of the global semantic of the original problem. Hence, we introduce in this paper a new global constraint dedicated to graph isomorphism problems, and we define an associated filtering algorithm that exploits all edges of the graphs in a global way to narrow variable domains. We then show how this global constraint can be decomposed into a set of ``distance'' constraints which propagate more domain reductions than ``edge'' constraints that are usually generated for this problem.