论文标题
五重奏Cayley图中的完美代码
Perfect codes in quintic Cayley graphs on abelian groups
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。在本文中，我们将所有连接的五重奏Cayley图表分类在接受完美代码的Abelian组上，并完全确定此类图的所有完美代码。
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 $C$. 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.
