The Square of Some Generalized Hamming Graphs

Article Computer Science, Theory & Methods

On the subgroup perfect codes in Cayley graphs

Yasamin Khaefi et al.

Summary: This paper examines the properties of perfect codes in finite groups. It is proven that if a group's Sylow 2-subgroup is a perfect code, then its subgroups are also perfect codes. This result holds for metabelian groups and nilpotent groups as well. The paper also classifies groups based on the formation of a chain of subgroup perfect codes and identifies groups with exactly two proper non-trivial subgroup perfect codes.

DESIGNS CODES AND CRYPTOGRAPHY (2023)

Add to Collection

Article Mathematics, Applied

Perfect state transfer in NEPS of complete graphs

Yipeng Li et al.

Summary: Perfect state transfer in graphs is a concept originating from quantum physics and quantum computing, involving the transfer of state between vertices at specific times. By analyzing the transition matrix of a graph, we can determine if the graph is periodic based on certain conditions.

DISCRETE APPLIED MATHEMATICS (2021)

Add to Collection

Article Quantum Science & Technology

Three-state quantum walk on the Cayley Graph of the Dihedral Group

Ying Liu et al.

Summary: The paper focuses on the three-state discrete-time quantum walk on the Caylay graph of the dihedral group, deriving analytic expressions for position probability distribution and long-time limit of the return probability. It is found that the localization effect is determined by the size of the underlying group, coin operator, and initial state. Numerical investigations are conducted on the model's properties through probability distribution and time-averaged probability at a specific position, showcasing the rich phenomena of three-state Grover DTQW on the Caylay graph of the dihedral group to aid in understanding and developing new quantum algorithms within the community.

QUANTUM INFORMATION PROCESSING (2021)

Add to Collection

Article Mathematics