Semiregularity and connectivity of the non- mathfrak F graph of a\n finite group

2021/09/09 by Andrea Lucchini, Lucchini, Andrea, Daniele Nemmi +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2109.04252

openalex publication_date 2021/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a class mathfrak F of finite groups, we consider the graph\n widetilde\Γ _{mathfrak F}(G) whose vertices are the elements of G and\nwhere two vertices g,h\∈ G are adjacent if and only if \⟨\ng,h\⟩\∉ mathfrak F. Moreover we denote by \I _mathfrak\nF(G) the set of the isolated vertices of widetilde\Γ _{mathfrak F}(G).\nWe address the following question: to what extent the fact that\n\I _{mathfrak F}(G) is a subgroup of H for any H\≤ G, implies\nthat the graph \Γ _{mathfrak F}G) obtained from\n widetilde\Γ _{mathfrak F}(G) by deleting the isolated vertices is a\nconnected graph?\n

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