Character graphs with diameter three

Mahdi Ebrahimi

Character graphs with diameter three

Group Theory 2019-09-10 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 show that if the diameter of $\Delta(G)$ is equal to three, then the complement of $\Delta(G)$ is bipartite. Also in this case, we determine the structure of the character graph $\Delta(G)$ .

Keywords

bipartite graphs character theory graph theory of groups

Cite

@article{arxiv.1909.03062,
  title  = {Character graphs with diameter three},
  author = {Mahdi Ebrahimi},
  journal= {arXiv preprint arXiv:1909.03062},
  year   = {2019}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1909.01180; text overlap with arXiv:1907.13292

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