On expander Cayley graphs from Galois rings
Combinatorics
2019-03-05 v3
Abstract
In this paper, we study new Cayley graphs over the additive group of Galois rings. First we prove that they are expander graphs by using a Weil-Carlitz-Uchiyama type estimation of character sums for Galois rings. We also show that Cayley graphs from Galois rings of characteristic 4 form a new infinite family of Ramanujan graphs by an elementary eigenvalue estimation. Moreover some other spectral properties of our graphs are also discussed.
Keywords
Cite
@article{arxiv.1902.03423,
title = {On expander Cayley graphs from Galois rings},
author = {Shohei Satake},
journal= {arXiv preprint arXiv:1902.03423},
year = {2019}
}
Comments
10 pages. The definition of the generalized Frobenius automorphism was corrected. The issue of new lines was fixed. The notation of constructed graphs was revised