Perfect codes in 2-valent Cayley digraphs on abelian groups

Abstract

For a digraph $\hat{I}“$, a subset $C$ of $V(\hat{I}“)$ is a perfect code if $C$ is a dominating set such that every vertex of $\hat{I}“$ is dominated by exactly one vertex in $C$. In this paper, we classify strongly connected 2-valent Cayley digraphs on abelian groups admitting a perfect code, and determine completely all perfect codes of such digraphs.

arXiv admin note: text overlap with arXiv:2207.06743