论文标题
有限简单组的非交通，非生成图
The non-commuting, non-generating graph of a finite simple group
论文作者
论文摘要
令$ g $为一个组，以至于$ g/z（g）$是有限且简单的。 $ g $的非交易，非生成图的$ g $的$ g $的$ g \ setminus z（g）$，边缘对应于不通勤和不产生$ g $的成对元素。为了补充我们对非简单群体这张图的调查，我们表明$ξ（g）$最多与直径相连，最多为$ 5 $，对于某些团体家庭来说，上限较小。然后，我们证明，当$ g $很简单时，$ g $的生成图的补充的直径具有$ 4 $的紧密上限，除了最多只有一个直径$ 5 $的组。
Let $G$ be a group such that $G/Z(G)$ is finite and simple. The non-commuting, non-generating graph $Ξ(G)$ of $G$ has vertex set $G \setminus Z(G)$, with edges corresponding to pairs of elements that do not commute and do not generate $G$. Complementing our previous investigation of this graph for non-simple groups, we show that $Ξ(G)$ is connected with diameter at most $5$, with smaller upper bounds for certain families of groups. Using these bounds, we then prove that when $G$ is simple, the diameter of the complement of the generating graph of $G$ has a tight upper bound of $4$, with the exception of at most one group with a graph of diameter $5$.
