Circulant Digraphs Integral over Number Fields
arXiv:1201.0798 · doi:10.1016/j.disc.2012.12.025
Abstract
A number field K is a finite extension of rational number field Q. A circulant digraph integral over K means that all its eigenvalues are algebraic integers of K. In this paper we give the sufficient and necessary condition for circulant digraphs which are integral over a number field K. And we solve the Conjecture3.3 in [XM] and find it is affirmative.
7 pages