The Cyclic Graph of a 2-Frobenius Group

2021/03/29 by David G. Costanzo, Mark L. Lewis, Costanzo, David G. +1 · 1 citation
Computer Science · Mathematics · #05C25 (secondary) #20C15 (primary) #FOS: Mathematics #Finite Group Theory Research #Graph Labeling and Dimension Problems #Graph theory and applications #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2103.15574

openalex publication_date 2021/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The cyclic graph of a group G is the graph whose vertices are the nonidentity elements of G and whose edges connect distinct elements x and y if and only if the subgroup ⟨ x,y⟩ is cyclic. We obtain information about the cyclic graph of 2-Frobenius groups. The cyclic graph of a 2-Frobenius group is disconnected. In this paper, we determine the number of connected components of the cyclic graph of any 2-Frobenius group.

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