The Commuting Graphs on Groups D2n and Qn
-
3518
Downloads
-
4827
Views
Authors
J. Vahidi
- Shomal University, Amol, Iran
A. Asghar Talebi
- University of mazandaran, babolsar, Iran
Abstract
Given group \(G\), the commuting graph of \(G\), is defined as the graph with vertex set \(G-Z(G)\), and
two distinct vertices \(x\) and \(y\) are connected by an edge, whenever they commute, that is \(xy=yx\). In
this paper we get some parameters of graph theory, as independent number and clique number for
groups \(D_{2n},Q_n\).
Share and Cite
ISRP Style
J. Vahidi, A. Asghar Talebi, The Commuting Graphs on Groups D2n and Qn, Journal of Mathematics and Computer Science, 1 (2010), no. 2, 123--127
AMA Style
Vahidi J., Talebi A. Asghar, The Commuting Graphs on Groups D2n and Qn. J Math Comput SCI-JM. (2010); 1(2):123--127
Chicago/Turabian Style
Vahidi, J., Talebi, A. Asghar. "The Commuting Graphs on Groups D2n and Qn." Journal of Mathematics and Computer Science, 1, no. 2 (2010): 123--127
Keywords
- independent number
- clique number
- generalized quaternion group
MSC
References
-
[1]
A. Abdollahi, S. Akbary, H. R. Maimani, Non-commuting graph of a group, J. Algebra, 298 (2006), 468--492
-
[2]
J. A. Bondy, U. S. R. Murty, Graph theory with applications, American Elsevier Publishing Co., New York (1976)
-
[3]
J. R. Moghadamfar, W. J. Shi, W. Zhou, A. R. Zokayi, On the non-commuting graph associated with a finite group, Sib. Math. J., 46 (2005), 325--332
-
[4]
Y. Segev, On finite homomorphic image of the multiplicative group of a division algebra, Ann. of Math., 149 (1999), 219--251
-
[5]
Y. Segev, G. M. Seitz, Anisotropic groups of type \(A_n\) and the commuting graph of finite simple groups, Pacific J. Math., 202 (2002), 125--225
-
[6]
A. Asghar Talebi, On the Non-commuting graphs of group \(D_{2n}\), International Journal of Algebra, International Journal of Algebra, 2 (2008), 957--961