On the Soluble Graph of a Finite Simple Group

Abstract

The maximal independent sets of the soluble graph of a finite simple group G are studied and their independence number is determined. In particular, it is shown that this graph in many cases has an independent set with three vertices.

Key Words:

• Finite simple group
• Grünberg-Kegel graph or prime graph
• Independence number
• Soluble graph

2010 Mathematics Subject Classification:

• 20D05
• 20D06

ACKNOWLEDGMENT

The authors like to thank the referee for many useful suggestions.

The second author is grateful to the Department of Mathematics of the University of Mainz for its warm hospitality during the time when this reseach was done. He also likes to thank the Deutsche Forschungsgemeinschaft and the RFBR (project 13-01-00469) for financial support.

Notes

Communicated by A. Olshanskii.