The algebraic degree of spectra of circulant graphs

JOURNAL OF NUMBER THEORY

卷:208

Article

Moenius, Katja¹ 

[1] Wurzburg Univ, Inst Math, Emil Fischer Str 40, D-97074 Wurzburg, Germany

关键词: Circulant graphs;    Graph spectrum;    Graph eigenvalues;    Algebraic degree;   

DOI  :  10.1016/j.jnt.2019.08.002

来源: Elsevier

【 摘 要 】

We investigate the algebraic degree of circulant graphs, i.e. the dimension of the splitting field of the characteristic polynomial of the associated adjacency matrix over the rationals. Studying the algebraic degree of graphs seems more natural than characterizing graphs with integral spectra only. We prove that the algebraic degree of circulant graphs on n vertices is bounded above by phi(n)/2, where phi denotes Euler's totient function, and that the family of cycle graphs provides a family of maximum algebraic degree within the family of all circulant graphs. Moreover, we precisely determine the algebraic degree of circulant graphs on a prime number of vertices. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free