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arXiv · 2002.03852

$K_n$-free Character Graphs with at Least $2n$ Vertices

Mahdi Ebrahimi
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Abstract

For a finite group $G$, let $\Delta(G)$ 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 $n$, $\Delta(G)$ is $K_n$-free, then $\Delta(G)$ 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.

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Mahdi Ebrahimi. 2020-02-06. $K_n$-free Character Graphs with at Least $2n$ Vertices. https://arxiv.org/abs/2002.03852

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