Proof of a conjecture of Abdollahi-Akbari-Maimani concerning the non-commutative graph of finite groups

2017/06/22 by Luis A. Dupont, Dupont, Luis A., Daniel G. Mendoza +3
Engineering · Mathematics · #05C25 #05C38 #05C45 #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Group Theory (math.GR) #graph theory and CDMA systems #math.GR #msc:05C25 #msc:05C38 #msc:05C45

paper · pdf · doi:10.48550/arxiv.1706.07142

The main result is false. It is an error

openalex publication_date 2017/06/22 · arxiv created 2017/09/20 · arxiv updated 2017/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The non--commuting graph Γ(G) of a non--abelian group G is defined as follows. The vertex set V(Γ(G)) of Γ(G) is G∖ Z(G) where Z(G) denotes the center of G and two vertices x and y are adjacent if and only if xy≠ yx. For non--abelian finite groups G and H it is conjectured that if Γ(G) ≅ Γ(H), then |G|=|H|. We prove the conjecture.

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