10 October 2023
Classifies nilpotent groups whose co-maximal subgroup graph is a cluster graph, triangle-free graph, claw-free graph, cograph, chordal graph, threshold graph
Determines values of n such that the dihedral group Dn and dicyclic group Q2n have certain forbidden subgraphs
Explores abelian groups whose co-maximal subgroup graph is chordal, cograph, threshold graph, or split graph
Uses concepts like forbidden subgraphs, adjacency, cycles, claw-free, and split graphs
Provides characterizations through multiple theorems and proofs
Forbidden subgraphs of co-maximal subgroup graphs
This paper explores co-maximal subgroup graphs of finite groups, characterizing which graphs have certain forbidden subgraphs like paths, cycles, and complete bipartite subgraphs. Through theorems and proofs, results are shown for nilpotent groups, dihedral groups, dicyclic groups, and abelian groups. The findings provide full classifications in many cases.
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