Research articles
ScienceAsia (): 231-235 |doi:
10.2306/scienceasia1513-1874...231
Generalization of the non-commuting graph of a group via a normal subgroup
Fereshteh Kakeria, Ahmad Erfanianb,*, Farzaneh Mansooria
ABSTRACT: Let G be a finite group and N be a normal subgroup of G. We define an undirected simple graph ΓN,G to be a graph whose vertex set is all elements in G∖ZN(G) and two vertices x and y are adjacent iff [x,y]∉N, where ZN(G)={g∈G:[x,g]∈N for all x∈G}. If N=1, then we obtain the known non-commuting graph of G. We give some basic results about connectivity, regularity, planarity, 1-planarity and some numerical invariants of the graph which are mostly improvements of the results given for non-commuting graphs. Also, a probability related to this graph is defined and a formula for the number of edges of the graph in terms of this probability is given.
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Ferdowsi University of Mashhad, International Campus, Mashhad, Iran |
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Department of Pure Mathematics and Centre of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, Mashhad, Iran |
* Corresponding author, E-mail: erfanian@math.um.ac.ir
Received 18 Feb 2015, Accepted 0 0000
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