直积的循环图（删除增强幂图）
The cyclic graph (deleted enhanced power graph) of a direct product
摘要：
设$G$是一个有限群.通过声明当且仅当$\langle x,y\rangle$是循环的时不同元素$x,y\in G^{\#}$是相邻的，在集合$G^{\#} = G \setminus \{ 1 \}$上定义一个图。用$Δ(G)$表示该图。图$Δ(G)$在文献中以循环图和删除增强功率图的名称出现。如果$G$和$H$是非平凡群，则$Δ(G\times H)$是完全刻划的。特别地，如果$Δ(G\times H)$是连接的，则获得直径界限以及满足该界限的示例。同时，建立了$Δ(G\times H)$不连通的充要条件.
英文摘要：
Let $G$ be a finite group. Define a graph on the set $G^{\#} = G \setminus \{ 1 \}$ by declaring distinct elements $x,y\in G^{\#}$ to be adjacent if and only if $\langle x,y\rangle$ is cyclic. Denote this graph by $Δ(G)$. The graph $Δ(G)$ has appeared in the literature under the names cyclic graph and deleted enhanced power graph. If $G$ and $H$ are nontrivial groups, then $Δ(G\times H)$ is completely characterized. In particular, if $Δ(G\times H)$ is connected, then a diameter bound is obtained, along with an example meeting this bound. Also, necessary and sufficient conditions for the disconnectedness of $Δ(G\times H)$ are established.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
