论文标题
直接产品的循环图（已删除的增强功率图）
The cyclic graph (deleted enhanced power graph) of a direct product
论文作者
论文摘要
令$ g $为有限的组。通过声明不同的元素$ x，y in g^{\＃} $在g^{\＃} $中，仅当$ x {\＃} $上，仅在$ \ langle x，y langle x，y \ rangle $ is Cyclic时，在$ g^{\＃} = g \ setMinus \ {1 \ {1 \ {1 \} $中。用$δ（g）$表示此图。图$δ（g）$以循环图的名称出现在文献中，并删除了增强功率图。如果$ g $和$ h $是非平凡的群体，则$δ（g \ times h）$是完全表征的。特别是，如果连接了$δ（g \ times h）$，则获得直径结合，以及一个符合此界限的示例。同样，还建立了$δ（g \ times h）$断开连接的必要条件。
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.
