A subset $C$ of the vertex set of a graph $\Gamma$ is called a perfect code of $\Gamma$ if every vertex of $\Gamma$ is at distance no more than one to exactly one vertex in $C$. Let $A$ be a finite abelian group and $T$ a square-free subset of $A$. The Cayley sum graph of $A$ with respect to the connection set $T$ is a simple graph with $A$ as its vertex set, and two vertices $x$ and $y$ are adjacent whenever $x+y\in T$. A subgroup of $A$ is said to be a subgroup perfect code of $A$ if the subgroup is a perfect code of some Cayley sum graph of $A$. In this paper, we give some necessary and sufficient conditions for a subset of $A$ to be a perfect code of a given Cayley sum graph of $A$. We also characterize all subgroup perfect codes of $A$.
@article{10_37236_9792,
author = {Xuanlong Ma and Kaishun Wang and Yuefeng Yang},
title = {Perfect codes in {Cayley} sum graphs},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {1},
doi = {10.37236/9792},
zbl = {1481.05070},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9792/}
}
TY - JOUR
AU - Xuanlong Ma
AU - Kaishun Wang
AU - Yuefeng Yang
TI - Perfect codes in Cayley sum graphs
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/9792/
DO - 10.37236/9792
ID - 10_37236_9792
ER -
%0 Journal Article
%A Xuanlong Ma
%A Kaishun Wang
%A Yuefeng Yang
%T Perfect codes in Cayley sum graphs
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/9792/
%R 10.37236/9792
%F 10_37236_9792
Xuanlong Ma; Kaishun Wang; Yuefeng Yang. Perfect codes in Cayley sum graphs. The electronic journal of combinatorics, Tome 29 (2022) no. 1. doi: 10.37236/9792
