The commuting graph of a soluble group

Abstract

The commuting graph of a finite soluble group with trivial centre is investigated. It is shown that the diameter of such a graph is at most 8 or the graph is disconnected. Examples of soluble groups with trivial centre and commuting graph of diameter 8 are provided.

Cited by in corpus (13)

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• Energy of commuting graph of finite groups whose centralizers are Abelian
• There is no upper bound for the diameter of the commuting graph of a finite group
• Various energies of some super integral groups
• Commuting graph of $A$-orbits
• On super integral groups
• Extending Morgan and Parker's results about commuting graphs
• The diameter of the commuting graph of a finite group with trivial centre
• Maximal Non-commuting Sets in Certain Unipotent Upper-triangular Linear Groups