ScienceAsia 41(2015): 73-78 |doi:
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: firstname.lastname@example.org
Received 24 Apr 2013, Accepted 21 Feb 2014