The Spectra of power graphs of certain finite groups

Abstract

The power graph of a group G is the graph with group elements as vertex set and two elements are adjacent if one is a power of the other. The aim of this paper is to compute the spectrum of the power graph of cyclic groups, dihedral groups, elementary abelian groups of prime power order and the Mathieu group .

Keywords:

• Graph spectrum
• cyclic group
• dihedral group
• elementary abelian group
• Mathieu group

AMS Subject Classifications:

• 05C25
• 05C50

Acknowledgements

We are indebted to the referees for their corrections and helpful remarks leaded us to rearrange the paper.

Additional information

Funding

The research of third author is partially supported by the University of Kashan under [grant number 464092/14].