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Research articles

ScienceAsia 41 (2015): 73-78 |doi: 10.2306/scienceasia1513-1874.2015.41.073

Some results on the power graphs of finite groups

Doostabadi Alireza, Erfanian Ahmad*, Jafarzadeh Abbas

ABSTRACT:     We classify planar graphs and complete power graphs of groups and show that the only infinite group with a complete power graph is the Prüfer group ℤp. Clique and chromatic numbers and the automorphism group of power graphs are investigated. We also prove that the reduced power graph of a group G is regular if and only if G is a cyclic p-group or exp(G)=p for some prime number p.

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Ferdowsi University of Mashhad, Department of Mathematics and Centre of Excellence in Analysis on Algebraic Structures, Mashhad, Iran

* Corresponding author, E-mail: erfanian@math.um.ac.ir

Received 24 Apr 2013, Accepted 21 Feb 2014