Superpower graphs of finite groups

Ajay Kumar, Lavanya Selvaganesh*, Peter J. Cameron, T. Tamizh Chelvam

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


For a finite group G, the superpower graph S(G) of G is an undirected simple graph with vertex set G and two vertices are adjacent in S(G) if and only if the order of one divides the order of the other in G. The aim of this paper is to provide tight bounds for the vertex connectivity, discuss Hamiltonian-like properties of superpower graph of finite non-abelian groups having an element of exponent order.

We also give some general results about superpower graphs and their relation to other graphs such as the Gruenberg–Kegel graph.
Original languageEnglish
JournalJournal of Algebra and Its Applications
VolumeOnline Ready
Early online date3 Apr 2024
Publication statusE-pub ahead of print - 3 Apr 2024


  • Superpower graph
  • Power graph
  • Hamiltonian cycle
  • Simple group
  • Vertex connectivity


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