Non-cyclic graphs of (non)orientable genus one

2015/12/03 by Xuanlong Ma, Ma, Xuanlong
Computer Science · Mathematics · #05C10 #05C25 #Advanced Graph Theory Research #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:05C10 #msc:05C25

paper · pdf · doi:10.48550/arxiv.1512.00935

9 pages, 3 figures

arxiv created 2015/12/03 · openalex publication_date 2015/12/03 · arxiv updated 2015/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite non-cyclic group. The non-cyclic graph Γ_G of G is the graph whose vertex set is G∖ Cyc(G), two distinct vertices being adjacent if they do not generate a cyclic subgroup, where Cyc(G)=\a∈ G: ⟨ a,b⟩ is cyclic for each b∈ G\. In this paper, we classify all finite non-cyclic groups G such that Γ_G has (non)orientable genus one.

Citations

• Commutative rings with toroidal zero-divisor graphs

Related

• Non-cyclic graph of a group
• Non-cyclic graph associated with a group
• Power graphs of (non)orientable genus two
• Finite groups with star-free noncyclic graphs
• On non-cyclic graph of finite groups