论文标题
关于非努力图理论的一些言论
A few remarks on the theory of non-nilpotent graphs
论文作者
论文摘要
我们证明了关于对称组的非努力图$ s_n $的一些结果 - 即，他们有一个汉密尔顿周期，并且满足了Nongsiang和Saikia的猜想。对于交替组$ a_n $，后者也是经过证明的。我们还表明，非磁性图类别没有任何“本地”属性，即。对于每一个简单的图形$ x $，都有一个$ g $，因此其非尼尔普特图具有$ x $作为诱导子图。
We prove a few results about non-nilpotent graphs of symmetric groups $S_n$ -- namely that they have a Hamiltonian cycle and they satisfy a conjecture of Nongsiang and Saikia. The latter is likewise proven for alternating groups $A_n$. We also show that the class of non-nilpotent graphs does not have any ''local'' properties, ie. for every simple graph $X$ there is a group $G$, such that its non-nilpotent graph has $X$ as an induced subgraph.
