Finite groups whose prime graphs are regular
Group Theory
2013-08-27 v2 Combinatorics
Representation Theory
Abstract
Let G be a finite group and let Irr(G) be the set of all irreducible complex characters of G. Let cd(G) be the set of all character degrees of G and denote by \rho(G) the set of primes which divide some character degrees of G. The prime graph \Delta(G) associated to G is a graph whose vertex set is \rho(G) and there is an edge between two distinct primes p and q if and only if the product pq divides some character degree of G. In this paper, we show that the prime graph \Delta(G) of a finite group G is 3-regular if and only if it is a complete graph with four vertices.
Cite
@article{arxiv.1307.2175,
title = {Finite groups whose prime graphs are regular},
author = {Hung P. Tong-Viet},
journal= {arXiv preprint arXiv:1307.2175},
year = {2013}
}
Comments
18 pages