Combinatorial necessary conditions for regular graphs to induce periodic quantum walks
Combinatorial necessary conditions for regular graphs to induce periodic quantum walks
复制标题
DOI：
10.1016/j.laa.2023.05.018
复制
发表时间：
2021-06
影响因子：
1.1
通讯作者：
Sho Kubota
中科院分区：
文献类型：
--
作者：
Sho Kubota
我们推导出由规则混合图定义的离散时间量子行走是周期性的组合必要条件。一个有用的必要条件是，如果具有 n 个顶点的 k-正则混合图是周期性的，则 2 n/k 必须是整数。作为这项工作的应用，我们确定了混合完全图和具有素数顶点的混合图的周期性。此外，我们研究了混合强正则图的周期性和几类混合距离正则图，并将现有结果扩展到混合图。
We derive combinatorial necessary conditions for discrete-time quantum walks defined by regular mixed graphs to be periodic. One useful necessary condition is that if a k-regular mixed graph with n vertices is periodic, then 2 n/k must be an integer. As an application of this work, we determine periodicity of mixed complete graphs and mixed graphs with a prime number of vertices. Furthermore, we study periodicity of mixed strongly regular graphs and several classes of mixed distance-regular graphs, and extend existing results to mixed graphs.