Regular character-graphs whose eigenvalues are greater than or equal to -2

DOI10.1016/J.DISC.2022.113137arXiv2107.05837MaRDI QIDQ6372635

Mahdi Ebrahimi, Maryam Khatami, Zohreh Mirzaei

Publication date: 13 July 2021

Abstract: Let $G$ be a finite group and $mathrmIrr(G)$ be the set of all complex irreducible characters of $G$. The character-graph $Delta(G)$ associated to $G$, is a graph whose vertex set is the set of primes which divide the degrees of some characters in $mathrmIrr(G)$ and two distinct primes $p$ and $q$ are adjacent in $Delta(G)$ if the product $pq$ divides $chi(1)$, for some $chiinmathrmIrr(G)$. Tong-viet posed the conjecture that if $Delta(G)$ is $k$-regular for some integer $kgeqslant2$, then $Delta(G)$ is either a complete graph or a cocktail party graph. In this paper, we show that his conjecture is true for all regular character-graphs whose eigenvalues are in the interval $[-2,infty)$.

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

This page was built for publication: Regular character-graphs whose eigenvalues are greater than or equal to -2

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6372635)