English

Regular graphs to induce even periodic Grover walks

Combinatorics 2023-07-26 v1

Abstract

The interest of this paper is a characterization of graphs that induce periodic Grover walks with given periods. In previous studies, Yoshie has shown that the only graphs that induce odd periodic Grover walks are cycle graphs. However, this problem is largely unsolved for even periods. In this study, we show that regular graphs that induce 2l2l-periodic Grover walks are also cycle graphs in most cases, where ll is an odd integer. The proof uses Galois theory.

Cite

@article{arxiv.2307.13227,
  title  = {Regular graphs to induce even periodic Grover walks},
  author = {Sho Kubota and Hiroto Sekido and Kiyoto Yoshino},
  journal= {arXiv preprint arXiv:2307.13227},
  year   = {2023}
}

Comments

16 pages

R2 v1 2026-06-28T11:39:17.192Z