Simple Groups Whose Gruenberg–Kegel Graph or Solvable Graph is Split

Mark L. Lewis, J. Mirzajani, A. R. Moghaddamfar, A. V. Vasil’ev, M. A. Zvezdina

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

A graph is split if there is a partition of its vertex set into a clique and an independent set. In this paper, we determine when the Gruenberg–Kegel graph, the solvable graph, and the compact forms of these graphs associated with finite nonabelian simple groups are split. In particular, it is proved that the compact form of the Gruenberg–Kegel graph of any finite simple group is split.

Original languageEnglish
Pages (from-to)2523-2547
Number of pages25
JournalBulletin of the Malaysian Mathematical Sciences Society
Volume43
Issue number3
DOIs
Publication statusPublished - 1 May 2020

Keywords

  • Gruenberg–Kegel graph
  • Simple group
  • Solvable graph
  • Split graph
  • RECOGNITION
  • ORDERS
  • FINITE-GROUPS
  • COMPONENTS
  • PRIME GRAPH
  • Gruenberg-Kegel graph

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