$K_4$-free character graphs with seven vertices

Mahdi Ebrahimi

$K_4$-free character graphs with seven vertices

Group Theory 2019-09-04 v1

Authors: Mahdi Ebrahimi

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 $G$ . In this paper, we determine the structure of all finite groups $G$ with $K_4$ -free character graph $\Delta(G)$ having seven vertices. We also obtain a classification of all $K_4$ -free graphs with seven vertices which can occur as character graphs of some finite groups.

Keywords

graph theory of groups graph theory character theory

Cite

@article{arxiv.1909.01180,
  title  = {$K_4$-free character graphs with seven vertices},
  author = {Mahdi Ebrahimi},
  journal= {arXiv preprint arXiv:1909.01180},
  year   = {2019}
}

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