至少有$2n$顶点的无$K_n$ Character图
$K_n$-free Character Graphs with at Least $2n$ Vertices
摘要：
对于有限群$G$，设$Δ(G)$表示建立在$G$的不可约复特征标的度集上的特征标图。Akhlaghi和Tong-Viet在\cite{[AT]}中指出，如果对某个正整数$n$，$Δ(G)$是$K_n$ -free的，则$Δ(G)$至多有$2n-1$顶点。在本文中，我们给出了一个例子来说明，这个猜想不一定对所有的非可解群成立，其特征标图是$K_n$ -free的。
英文摘要：
For a finite group $G$, let $Δ(G)$ denote the character graph built on the set of degrees of the irreducible complex characters of $G$. Akhlaghi and Tong-Viet in \cite{[AT]} conjectured that if for some positive integer $n$, $Δ(G)$ is $K_n$-free, then $Δ(G)$ has at most $2n-1$ vertices. In this paper, we present an example to show that this conjecture is not necessarily true for all non-solvable groups whose character graphs are $K_n$-free.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
