On spectral radii of Coxeter transformations Original Research Article

Let T be a finite tree and dT the maximal (branching) degree of its vertices. Let ρT be the spectral radius of a Coxeter transformation defined by T. ThenimageρT<4dT−6.This is a substantial improvement of an existing quadratic bound dT2−2. Furthermore, image for dT>5. The upper bound is derived from an upper bound for the spectral radius of the adjacency matrix of T. In fact, our method can be used to establish a more efficient upper bound for the spectral radii of Coxeter transformations defined by particular graphs, as well as to establish a general upper bound in the case of arbitrary valued trees replacing the degree dT by a valued degree image.