ON BOUNDED AUTOMORPHISMS OF LOCALLY FINITE TRANSITIVE GRAPHS

The automorphism-group of an infinite graph acts in a natural way on t he set of d-fibers (components of the set of rays with respect to the Hausdorff metric). For connected, locally finite, almost transitive gr aphs the kernel of this action is proved to be the group of bounded au tomorphisms. This completes a result of Moller, who characterized the bounded automorphisms of connected, locally finite, transitive graphs with infinitely many ends. (C) 1996 John Wiley & Sons, Inc.