论文标题
$ g $ - 相对于其子组的有限组的noncmumting图
$g$-noncommuting graph of a finite group relative to its subgroups
论文作者
论文摘要
令$ h $为有限的非亚洲集团$ g $和$ g \ in G $的子组。令$ z（h，g）= \ {x \ in H：xy = yx，\ forall y \ in G \ \} $。我们介绍了图$δ_{h，g}^g $，其顶点集为$ g \ setMinus z（h，g）$，如果$ x \ in H $或$ y \ in H $和$ y \ in H $和$和$ y和$ y \ in $和$ [x，y] \ y] x^{ - 1} y^{ - 1} xy $。在本文中，我们确定$δ_{h，g}^g $是否是其他结果。我们还讨论了其直径和连通性，并特别注意二面体群体。
Let $H$ be a subgroup of a finite non-abelian group $G$ and $g \in G$. Let $Z(H, G) = \{x \in H : xy = yx, \forall y \in G\}$. We introduce the graph $Δ_{H, G}^g$ whose vertex set is $G \setminus Z(H, G)$ and two distinct vertices $x$ and $y$ are adjacent if $x \in H$ or $y \in H$ and $[x,y] \neq g, g^{-1}$, where $[x,y] = x^{-1}y^{-1}xy$. In this paper, we determine whether $Δ_{H, G}^g$ is a tree among other results. We also discuss about its diameter and connectivity with special attention to the dihedral groups.
