$K_n$-free Character Graphs with at Least $2n$ Vertices
Group Theory
2020-02-18 v2
Abstract
For a finite group , let denote the character graph built on the set of degrees of the irreducible complex characters of . Akhlaghi and Tong-Viet in \cite{[AT]} conjectured that if for some positive integer , is -free, then has at most 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 -free.
Cite
@article{arxiv.2002.03852,
title = {$K_n$-free Character Graphs with at Least $2n$ Vertices},
author = {Mahdi Ebrahimi},
journal= {arXiv preprint arXiv:2002.03852},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:2002.01353. The counterexample given in this manuscripts has been presented in [Bounding the number of vertices in the degree graph of a finite group, Z. Akhlaghi, S. Dolfi, E. Pacifici, L. Sanus, Journal of Pure and Applied Algebra, 224(2020) 725-731