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 .

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Coxeter transformation; Spectral radius; Coxeter polynomial; Generalized Cartan matrix; Valued tree |

Subjects: | Q Science / természettudomány > QA Mathematics / matematika > QA72 Algebra / algebra |

SWORD Depositor: | MTMT SWORD |

Depositing User: | MTMT SWORD |

Date Deposited: | 10 Mar 2014 10:56 |

Last Modified: | 10 Mar 2014 10:56 |

URI: | http://real.mtak.hu/id/eprint/10769 |

### Actions (login required)

Edit Item |