Work

Perfect codes in quartic Cayley graphs of generalized dihedral groups

Year: 2025

Type: preprint

Abstract: For a graph $Γ=(VΓ,EΓ)$, a subset $D$ of $VΓ$ is a perfect code in $Γ$ if every vertex of $Γ$ is dominated by exactly one vertex in $D$. In this paper, we classify all connected quartic Cayley graphs on generalized dihedral groups admitting a perfect code, and determine all perfect codes in such graphs.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2505.19677

Authors: Dong, Chengcheng, Yang, Yuefeng, Dong, Changchang

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities

Awards: G3092466398, G8798946080

OpenAlex ID: W4416557664

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