English

Perfect codes in quintic Cayley graphs on abelian groups

Combinatorics 2024-06-04 v4

Abstract

A subset CC of the vertex set of a graph Γ\Gamma is called a perfect code of Γ\Gamma if every vertex of Γ\Gamma is at distance no more than one to exactly one vertex in CC. In this paper, we classify all connected quintic Cayley graphs on abelian groups that admit a perfect code, and determine completely all perfect codes of such graphs.

Keywords

Cite

@article{arxiv.2207.06743,
  title  = {Perfect codes in quintic Cayley graphs on abelian groups},
  author = {Yuefeng Yang and Xuanlong Ma and Qing Zeng},
  journal= {arXiv preprint arXiv:2207.06743},
  year   = {2024}
}
R2 v1 2026-06-25T00:54:27.807Z