On the character degree graph of finite groups
Group Theory
2018-09-28 v1
Abstract
Given a finite group G, let cd(G) denote the set of degrees of the irreducible complex characters of G. The character degree graph of G is defined as the simple undirected graph whose vertices are the prime divisors of the numbers in cd(G), two distinct vertices p and q being adjacent if and only if pq divides some number in cd(G). In this paper, we consider the complement of the character degree graph, and we characterize the finite groups for which this complement graph is not bipartite. This extends the analysis of [1], where the solvable case was treated.
Keywords
Cite
@article{arxiv.1809.10415,
title = {On the character degree graph of finite groups},
author = {Zeinab Akhlaghi and Carlo Casolo and Silvio Dolfi and Emanuele Pacifici and Lucia Sanus},
journal= {arXiv preprint arXiv:1809.10415},
year = {2018}
}