The coprime graph of a group

Document Type : Research Paper


1 Beijing Normal University

2 Guangxi University

3 Guangxi Teachers Education University


The coprime graph $\gg$ with a finite group $G$‎ ‎as follows‎: ‎Take $G$ as the vertex set of $\gg$ and join two distinct‎ ‎vertices $u$ and $v$ if $(|u|,|v|)=1$‎. ‎In the paper‎, ‎we explore how the graph‎ ‎theoretical properties of $\gg$ can effect on the group theoretical‎ ‎properties of $G$‎.


Main Subjects

A. Abdollahi, S. Akbari and H. R. Maimani (2006). Non-commuting graph of a group. J. Algebra. 298, 468-492 A. Abdollahi and A. M. Hassanabadi (2007). Non-cyclic graph of a group. Comm. Algebra. 35, 2057-2081 P. Balakrishnan, M. Sattanathan and R. Kala (2011). The center graph of a group. South Asian J. Math.. 1, 21-28 I. Chakrabarty, S. Ghosh and M. Sen (2009). Undirected power graphs of semigroups. Semigroup Forum. 78, 410-426 C. Gary and P. Zhang (2006). Introduction to Graph Theory. Posts and Telecom Press, Beijing. M. S. Lucido (1999). Prime graph components of finite almost simple groups. Rend. Sem. Mat. Univ. Padova. 102, 1-22 X. L. Ma, H. Q. Wei and G. Zhong (2013). The cyclic graph of a finite group. Algebra, Article ID 107265, {}. 2013 H. Kurzweil and B. Stellmacher (2004). The Theory of Finite Groups An Introduction. Springer-Verlag, New York.
Volume 3, Issue 3 - Serial Number 3
September 2014
Pages 13-23
  • Receive Date: 08 November 2012
  • Revise Date: 10 October 2013
  • Accept Date: 22 January 2014
  • Published Online: 01 September 2014