Rationality conditions for the eigenvalues of normal finite Cayley graphs
Combinatorics
2014-02-25 v1 Group Theory
Abstract
Given a finite group G, we say that a subset C of G is power-closed if, for every x in C and y in <x> with <x>=<y>, we have that y lies in C. In this paper we are interested in finite Cayley digraphs Cay(G,C) over G with connection set C, where C is a union of conjugacy classes of G. We show that each eigenvalue of Cay(G,C) is integral if and only if C is power-closed. This result will follow from a discussion of some more general rationality conditions on the eigenvalues of Cay(G,C).
Keywords
Cite
@article{arxiv.1402.5494,
title = {Rationality conditions for the eigenvalues of normal finite Cayley graphs},
author = {Chris Godsil and Pablo Spiga},
journal= {arXiv preprint arXiv:1402.5494},
year = {2014}
}