Title : ( Some results on the power graph of finite groups )
Authors: alireza doostabadi , Ahmad Erfanian , Abbas Jafarzadeh ,
Full TextAbstract
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 Z_{p^∞}. 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.
Keywords
, reduced power graph, planar graph, perfect graph, regular graph, automorphism group of a graph
@article{paperid:1059541,
author = {Doostabadi, Alireza and Erfanian, Ahmad and Jafarzadeh, Abbas},
title = {Some results on the power graph of finite groups},
journal = {ScienceAsia},
year = {2015},
volume = {41},
number = {1},
month = {February},
issn = {1513-1874},
pages = {73--78},
numpages = {5},
keywords = {reduced power graph; planar graph; perfect graph; regular graph; automorphism group of a graph},
}
%0 Journal Article
%T Some results on the power graph of finite groups
%A Doostabadi, Alireza
%A Erfanian, Ahmad
%A Jafarzadeh, Abbas
%J ScienceAsia
%@ 1513-1874
%D 2015
