Perfect Codes in Cayley Sum Graphs
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Published:2022-01-28
Issue:1
Volume:29
Page:
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ISSN:1077-8926
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Container-title:The Electronic Journal of Combinatorics
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language:
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Short-container-title:Electron. J. Combin.
Author:
Ma Xuanlong,Wang Kaishun,Yang Yuefeng
Abstract
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 $A$.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
1 articles.
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