Finite groups whose commuting graph is split

Xuanlong Ma*, Peter J. Cameron

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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As a contribution to the study of graphs defined on groups, we show that for a finite group G the following statements are equivalent: the commuting graph of G is a split graph; the commuting graph of G is a threshold graph; either G is abelian, or G is a generalized dihedral group D(A)=⟨A,t:(∀a∈A)(at)2=1⟩ where A is an abelian group of odd order.
Original languageEnglish
Pages (from-to)280-283
JournalTrudy Instituta Matematiki i Mekhaniki UrO RAN
Issue number1
Publication statusPublished - 4 Mar 2024


  • Commuting graph
  • Split graph
  • Threshold graph
  • Generalized dihedral group


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