2021/07/13 by Mahdi Ebrahimi, Ebrahimi, Mahdi, Maryam Khatami +3
Chemistry · Mathematics · Medicine · #05C25 #05C50 #20C15 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Metal complexes synthesis and properties #Synthesis and Reactivity of Heterocycles
paper · pdf · doi:10.48550/arxiv.2107.05837
openalex publication_date 2021/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a finite group and Irr(G) be the set of all complex irreducible characters of G. The character-graph Δ(G) associated to G, is a graph whose vertex set is the set of primes which divide the degrees of some characters in Irr(G) and two distinct primes p and q are adjacent in Δ(G) if the product pq divides χ(1), for some χ\inIrr(G). Tong-viet posed the conjecture that if Δ(G) is k-regular for some integer k\geqslant 2, then Δ(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, ∞ ).