The compatible action graphs for finite cyclic 2-groups

Authors

  • S.A. Sulaiman Universiti Malaysia Pahang
  • M.S. Mohamed Universiti Malaysia Pahang
  • Y. Yusof Universiti Malaysia Pahang
  • M.K. Shahoodh Al-Ramadi Education/Al-Idresi Secondray School for Girls
  • H.A. Hamid Universiti Malaysia Perlis

DOI:

https://doi.org/10.15282/daam.v1i01.5111

Keywords:

Compatible action, cyclic group, compatible action graph, the nonabelian tensor product

Abstract

A graph namely the compatible action graph is introduced by extending the results on the compatible pairs of actions for cyclic 2-groups. Some properties of compatible action graphs are presented. In addition, the special types of compatible action graphs are given.

References

Brown R, Johnson DL, Robertson E. Some computations of non-abelian tensor products of groups. Journal of Algebra. 1987 Nov 1;111(1):177-202.

Visscher MP. On the nonabelian tensor product of groups. State University of New York at Binghamton; 1998.

Mohamad MS. Compatibility conditions and nonabelian tensor products of finite cyclic groups of p-power order (Doctoral dissertation, PhD Dissertation, Universiti Teknologi Malaysia,2012).

Sulaiman SA, Mohamad MS, Yusof Y, Shahoodh MK. The Number of Compatible Pair of Actions for Cyclic Groups of 2-Power Order. International Journal of Simulation, System, Sciences and Technology. 2017 Dec 1;18(4):1473-8031.

Shahoodh MK, Mohamad MS, Yusof Y, Sulaiman SA. Number of Compatible Pair of Actions for Finite Cyclic Groups of 3-Power Order. International Journal of Simulation, System, Sciences and Technology. 2017; 18(4).

Mohamad MS, Sulaiman SA, Yusof Y, Shahoodh MK. Compatible pair of actions for two same cyclic groups of 2-power order. In: Journal of Physics: Conference Series 2017 Sep 1 (Vol. 890, No. 1, p. 012120). IOP Publishing.

Sulaiman SA, Mohamad MS, Yusof Y, Shahoodh MK. The Number of Compatible Pair of Actions for Cyclic Groups of 2-Power Order. International Journal of Simulation, System, Sciences and Technology. 2017 Dec 1;18(4):1473-8031.

Abdollahi A, Akbari S, Maimani HR. Non-commuting graph of a group. Journal of Algebra. 2006 Apr 15;298(2):468-92.

Darafsheh MR. Groups with the same non-commuting graph. Discrete Applied mathematics. 2009 Feb 28;157(4):833-7.

Jahandideh M, Darafsheh MR, Sarmin NH, Omer SM. Conditions on the edges and vertices of non-commuting graph. J. Tech. 2015;74(1):73-6.

Mansoori F, Erfanian A, Tolue B. Non-coprime graph of a finite group. In: AIP Conference Proceedings 2016 Jun 21 (Vol. 1750, No. 1). AIP Publishing.

Shahoodh MK, Mohamad MS, Yusof Y, Sulaiman SA. Subgraph of Compatible Action Graph for Finite Cyclic Groups of p-Power Order. InJournal of Physics: Conference Series 2019 Nov 1 (Vol. 1366, No. 1, p. 012064). IOP Publishing.

Bollobás B. Modern graph theory. Springer Science & Business Media; 2013 Dec 1.

Downloads

Published

2020-12-01

How to Cite

Sulaiman, S., Mohamed, M., Yusof, Y., Shahoodh, M., & Hamid, H. (2020). The compatible action graphs for finite cyclic 2-groups. Data Analytics and Applied Mathematics (DAAM), 1(1), 23–30. https://doi.org/10.15282/daam.v1i01.5111

Issue

Section

Research Articles