On the clique number of non-commuting graphs of certain groups
| dc.creator | Abdollahi, A. | |
| dc.creator | Azad, A. | |
| dc.creator | Hassanabadi, A. Mohammadi | |
| dc.creator | Zarrin, M. | |
| dc.date | 2009-03-04 | |
| dc.date.accessioned | 2026-07-07T12:48:58Z | |
| dc.date.available | 2026-07-07T12:48:58Z | |
| dc.description | Let $G$ be a non-abelian group. The non-commuting graph $\mathcal{A}_G$ of $G$ is defined as the graph whose vertex set is the non-central elements of $G$ and two vertices are joint if and only if they do not commute. In a finite simple graph $Γ$ the maximum size of a complete subgraph of $Γ$ is called the clique number of $Γ$ and it is denoted by $ω(Γ)$. In this paper we characterize all non-solvable groups $G$ with $ω(\mathcal{A}_G)\leq 57$, where the number 57 is the clique number of the non-commuting graph of the projective special linear group $\mathrm{PSL}(2,7)$. We also complete the determination of $ω(\mathcal{A}_G)$ for all finite minimal simple groups. | |
| dc.description | to appear in Algebra Colloquium | |
| dc.identifier | https://arxiv.org/abs/0903.0692 | |
| dc.identifier | http://arxiv.org/abs/0903.0692 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222246 | |
| dc.subject | Group Theory | |
| dc.subject | 20D60 | |
| dc.title | On the clique number of non-commuting graphs of certain groups | |
| dc.type | text |