Work

Regular graphs to induce even periodic Grover walks

Year: 2024

Type: article

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 2 l -periodic Grover walks are also cycle graphs in most cases, where l is an odd integer. The proof uses Galois theory.

Source: Discrete Mathematics

DOI: 10.1016/j.disc.2024.114345

Authors: Sho Kubota, Hiroto Sekido, Kiyoto Yoshino

Institutions: Osaka Institute of Technology, Yokohama National University, Hiroshima Institute of Technology

Language: English

Topic: Graph theory and applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,120

Funder: Japan Society for the Promotion of Science