Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $K_n$-free Character Graphs with at Least $2n$ Vertices   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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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci