Minimal cut-sets in the power graphs of certain finite non-cyclic groups

Abstract

We study minimal cut-sets of the power graph of a finite non-cyclic nilpotent group which are associated with its maximal cyclic subgroups. As a result, we find the vertex connectivity of the power graphs of certain finite non-cyclic abelian groups whose order is divisible by at most three distinct primes.

Keywords:

• Generalized quaternion group
• Minimal cut-set
• Nilpotent group
• Power graph
• Vertex connectivity

AMS SUBJECT CLASSIFICATION (2010):

• 05C25
• 05C40
• 20D15
• 20K01

Acknowledgments

The authors wish to sincerely thank the referee for his/her detailed comments and suggestions, thus improving the submitted version of the article.

Additional information

Funding

The author Binod Kumar Sahoo was partially supported by Project No. MTR/2017/000372 of the Science and Engineering Research Board (SERB), Department of Science and Technology, Government of India.