论文标题
有限组的相对G-Noncommuting图
Relative g-noncommuting graph of finite groups
论文作者
论文摘要
令$ g $为有限的组。 For a fixed element $g$ in $G$ and a given subgroup $H$ of $G$, the relative $g$-noncommuting graph of $G$ is a simple undirected graph whose vertex set is $G$ and two vertices $x$ and $y$ are adjacent if $x \in H$ or $y \in H$ and $[x,y] \neq g, g^{-1}$.我们用$γ_{h，g}^g $表示此图。在本文中，我们获得了$γ_{h，g}^g $中任何顶点的计算公式，并表征$γ_{h，g}^g $是树，星形图，lollipop还是完整的图形，或者与$γ_{h，g}^g $ wimsomorphism的某些属性以及某些属性。我们还介绍了$γ_{h，g}^g $中边数与$ g $的某些通用通勤概率之间的某些关系，这些概率为$γ_{h，g}^g $中边缘数的一些计算公式提供了一些计算公式。最后，我们通过在$γ_{h，g}^g $中得出一些边数的界限来结束本文。
Let $G$ be a finite group. For a fixed element $g$ in $G$ and a given subgroup $H$ of $G$, the relative $g$-noncommuting graph of $G$ is a simple undirected graph whose vertex set is $G$ and two vertices $x$ and $y$ are adjacent if $x \in H$ or $y \in H$ and $[x,y] \neq g, g^{-1}$. We denote this graph by $Γ_{H, G}^g$. In this paper, we obtain computing formulae for degree of any vertex in $Γ_{H, G}^g$ and characterize whether $Γ_{H, G}^g$ is a tree, star graph, lollipop or a complete graph together with some properties of $Γ_{H, G}^g$ involving isomorphism of graphs. We also present certain relations between the number of edges in $Γ_{H, G}^g$ and certain generalized commuting probabilities of $G$ which give some computing formulae for the number of edges in $Γ_{H, G}^g$. Finally, we conclude this paper by deriving some bounds for the number of edges in $Γ_{H, G}^g$.
