On bounds of spectral radii of of Coxeter

Lakatos, Piroska and Dlab, V. (2003) On bounds of spectral radii of of Coxeter. LINEAR ALGEBRA AND ITS APPLICATIONS, 365. pp. 143-153. ISSN 0024-3795

Text 1220954.pdf Restricted to Repository staff only Download (425kB) | Request a copy

Abstract

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. Then ρT < 4dT − 6. This is a substantial improvement of an existing quadratic bound d2 T − 2. Furthermore, ρT > dT − 21 10 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 ¯ dT .

Actions (login required)

Edit Item