K_n-free Character Graphs with at Least 2n Vertices

2020/02/06 by Mahdi Ebrahimi, Ebrahimi, Mahdi
Engineering · Mathematics · #05C25 #20C15 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2002.03852

openalex publication_date 2020/02/06 · openalex created_date 2020/02/14 · openalex updated_date 2026/07/28

Abstract

For a finite group G, let Δ(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, Δ(G) is K_n-free, then Δ(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.

Related

• K₄-free character graphs with seven vertices
• On the character degree graph of solvable groups
• n-exact Character Graphs
• K₄-free character graphs with diameter three
• Regular character-graphs whose eigenvalues are greater than or equal to -2