On non-cyclic graph of finite groups

2016/09/23 by Ebrahim Vatandoost, Vatandoost, Ebrahim, Yasser Golkhandy Pour +1
Computer Science · Engineering · Mathematics · #05c25 #Advanced Graph Theory Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1609.07247

openalex publication_date 2016/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Here we study some algebraic properties of non-cyclic graphs. In this paper we show that Γ_G is isomorphic to K₃∪ (n-4)K₁ or K₄∪ (n-5)K₁ if and only if G is isomorphic to D₈ or D₁₀, respectively. We characterize all groups of order n like G in which γ(Γ_G)+γ(Γ_G)∈ \n, n-1, n-2, n-3\, where |Cyc(G)|=1.

Related

• Non-cyclic graph of a group
• Non-cyclic graph associated with a group
• Finite groups with star-free noncyclic graphs
• Non-cyclic graphs of (non)orientable genus one
• Graphs encoding the generating properties of a finite group