Co-maximal subgroup graph characterized by forbidden subgraphs

2023/10/10 by Pallabi Manna, Manna, Pallabi, Santanu Mandal +3
Engineering · Materials Science · Mathematics · #05C25 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Synthesis and properties of polymers #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2310.06392

openalex publication_date 2023/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this communication, the co-maximal subgroup graph Γ(G) of a finite group G is examined when G is a finite nilpotent group, finite abelian group, dihedral group D_n, dicyclic group Q_2ⁿ, and p-group. We derive the necessary and sufficient conditions for Γ(G) to be a cluster graph, triangle-free graph, claw-free graph, cograph, chordal graph, threshold graph and split graph. For the case of finite nilpotent group, we are able to classify it entirely. Moreover, we derive the complete structure of finite abelian group G such that Γ(G) is a split graph. We leave the readers with a few unsolved questions.

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