论文标题
Cayley Sum图中的完美代码
Perfect codes in Cayley sum graphs
论文作者
论文摘要
如果$γ$的每个顶点的距离不超过一个$ c $的一个顶点，则图$γ$的顶点$ c $称为$γ$的完美代码。让$ a $为有限的阿贝尔集团，每平方英尺的$ a $ a $ $ a $。相对于连接集$ t $的Cayley Sum图是一个简单的图表，$ a $作为其顶点集，并且每当t $中的$ x+y \时，两个顶点$ x $和$ y $都相邻。如果子组是$ a $的某些cayley sum图的完美代码，则据说$ a $的子组是$ a $的子组完美代码。在本文中，我们为$ a $的子集提供了一些必要和足够的条件，以作为给定的Cayley Sum $ a $的完美代码。我们还表征了$ a $的所有子组完美代码。
A subset $C$ of the vertex set of a graph $Γ$ is called a perfect code of $Γ$ if every vertex of $Γ$ 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 $A$.
