论文标题
断开的字符图和奇数主导集
Disconnected Character graphs and odd Dominating sets
论文作者
论文摘要
假设$γ$是有限的简单图。如果$ d $是$γ$的主要集合，以便d $中的每个$ x \都包含在$γ$的奇数循环的一组顶点中，那么我们说$ d $是$γ$的奇数主导套装。对于有限的$ g $，让$δ（g）$表示构建的字符图，构建在$ g $的不可约合复杂字符的一组。在本文中，我们表明$δ（g）$的补体包含一个奇数的统治集，并且仅当$δ（g）$是一个脱节的图表，并具有非双方补体的断开图。
Suppose $Γ$ is a finite simple graph. If $D$ is a dominating set of $Γ$ such that each $x\in D$ is contained in the set of vertices of an odd cycle of $Γ$, then we say that $D$ is an odd dominating set for $Γ$. For a finite group $G$, let $Δ(G)$ denote the character graph built on the set of degrees of the irreducible complex characters of $G$. In this paper, we show that the complement of $Δ(G)$ contains an odd dominating set, if and only if $Δ(G)$ is a disconnected graph with non-bipartite complement.
