Finite groups with star-free noncyclic graphs

2016/04/24 by Xuanlong Ma, Ma, Xuanlong, Gary L. Walls +3
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1604.06978

openalex publication_date 2016/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a finite noncyclic group G, let \Cyc(G) be a set of elements a of G such that ⟨ a,b⟩ is cyclic for each b of G. The noncyclic graph of G is a graph with the vertex set G∖ \Cyc(G), having an edge between two distinct vertices x and y if ⟨ x, y⟩ is not cyclic. In this paper, we classify all finite noncyclic groups whose noncyclic graphs are K_1,n-free, where 3≤ n≤ 6.

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