论文标题
在有限循环基团的功率图的最小切割机上
On the minimum cut-sets of the power graph of a finite cyclic group
论文作者
论文摘要
有限组$ g $的电源图$ \ MATHCAL {p}（g）$是带有顶点套装$ g $的简单图，如果其中一个是另一个的力量，则两个不同的顶点相邻。对于整数$ n \ geq 2 $，令$ c_n $表示订单$ n $的环状群体，让$ r $是$ n $的独特prime分隔线的数量。 $ \ mathcal {p}（c_n）$的最小切割集在\ cite {cps}中以$ r \ leq 3 $为特征。在本文中，对于$ r \ geq 4 $，我们确定了$ \ mathcal {p}（p}（c_n）$的某些切割组，以便任何最小切割$ \ nathcal {p}（c_n）$都必须是其中之一。
The power graph $\mathcal{P}(G)$ of a finite group $G$ is the simple graph with vertex set $G$, in which two distinct vertices are adjacent if one of them is a power of the other. For an integer $n\geq 2$, let $C_n$ denote the cyclic group of order $n$ and let $r$ be the number of distinct prime divisors of $n$. The minimum cut-sets of $\mathcal{P}(C_n)$ are characterized in \cite{cps} for $r\leq 3$. In this paper, for $r\geq 4$, we identify certain cut-sets of $\mathcal{P}(C_n)$ such that any minimum cut-set of $\mathcal{P}(C_n)$ must be one of them.
