Regular graphs to induce even periodic Grover walks

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-11-29 DOI:10.1016/j.disc.2024.114345

Sho Kubota , Hiroto Sekido , Kiyoto Yoshino

引用次数: 0

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

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正则图来诱导周期格罗弗行走

本文的兴趣是对具有给定周期的格罗弗周期行走图的刻画。在之前的研究中，Yoshie已经证明了唯一能引起奇周期格罗弗行走的图是循环图。然而，这个问题在很大程度上没有得到解决。在本研究中，我们证明了在大多数情况下，引起2l周期Grover行走的正则图也是循环图，其中l是一个奇数。证明使用伽罗瓦理论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.