Title of article :
On the commuting graph of some non-commutative rings with unity
Author/Authors :
Vatandoost, E. Department of Basic science - Imam Khomeini International University, Qazvin, Iran , Ramezani, F. Department of Basic science - Imam Khomeini International University, Qazvin, Iran
Abstract :
Let R be a non-commutative ring with unity. The commuting graph of R denoted
by (R), is a graph with a vertex set R n Z(R) and two vertices a and b are adjacent if and only if ab = ba. In this paper, we investigate non-commutative rings with unity of order pn where p is prime and n 2 f4; 5g. It is shown that, (R) is the disjoint union of complete graphs. Finally, we prove that there are exactly ve commuting graphs of non-commutative rings with unity up to twenty vertices and they are 3K2; 3K4; 7K2;K2 [ 2K6 and 4K2 [K6.
Keywords :
Commuting graphs , non-commutative rings , non-connected graphs
Journal title :
Astroparticle Physics