Research articles
ScienceAsia 45 (2019): 482487 doi:
10.2306/scienceasia15131874.2019.45.482
Some results on the noncommuting graph of a finite
group
K. Moradipour^{a,*}, Sh. Ilangovan^{b}, S. Rashid^{c}
ABSTRACT: Let G be a metacyclic pgroup, and let Z(G) be its center. The noncommuting graph Γ_{G} of a metacyclic pgroup G is defined as the graph whose vertex set is G−Z(G), and two distinct vertices x and y are connected by an edge
if and only if the commutator of x and y is not the identity. In this paper, we give some graph theoretical properties
of the noncommuting graph Γ_{G}. Particularly, we investigate planarity, completeness, clique number and chromatic
number of such graph. Also, we prove that if G_{1} and G_{2} are isoclinic metacyclic pgroups, then their associated graphs
are isomorphic.
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^{a} 
Department of Mathematics, Faculty of Khorramabad, Lorestan Branch,
Technical and Vocational University, Iran 
^{b} 
The University of Nottingham Malaysia Campus Jalan Broga, 43500 Semenyih Selangor Darul Ehsan,
Malaysia 
^{c} 
Department of Mathematics, College of Basic Sciences, YadegareImam Khomeini (RAH) Branch,
Islamic Azad University, Tehran, Iran 
* Corresponding author, Email: kayvanmrp@yahoo.com
Received 14 Apr 2019, Accepted 20 Aug 2019
