Non-Compatible Action Graph and Its Adjacency Matrix for The Non-abelian Tensor Product for Groups of Prime Power Order

Authors

  • mohd Shahoodh ministry of education

DOI:

https://doi.org/10.31185/wjcms.204

Abstract

This article focused on the notion of the non-abelian tensor product of groups of prime power order. Particularly, it presented new graph named as Non-compatible action graph and discussed some of its properties. Moreover, this graph concentrated on the case of non-compatible actions of the tensor product of two finite -groups. Furthermore, its adjacency matrix has been determined and discussed in detail. Moreover, the adjacency matrix has been denoted by A(G) and its inputs are 1 whenever there is adjacency and 0 otherwise. 

References

J. C. M. Pezzott and I. N. Nakaoka, "Commuting Graph of a Group on a Transversal," arXiv preprint arXiv:1807.01821,pp.1-14, 2018.

A. Abdollahi, S. Akbari and H. R. Maimani, "Non-commuting Graph of a Group," Journal of Algebra, vol. 298, pp. 468-492, 2006.

E. A. Bertram, M. Herzog and A. Mann, "On Graph Related to Conjugacy Classes of Groups," Bulletin of the London Mathematical Society, vol. 22, no. 6, pp. 569-575, 1990.

T. Chalapath and R. K. Kumar, "Neutrosophic Graphs of Finite Groups," Neutrosophic Sets and Systems, vol.15, pp. 22-30, 2017.

M. K. Shahoodh, M. S. Mohamad, Y. Yusof, S. A. Sulaiman and N. H. Sarmin, "Compatible Action Graph for Finite Cyclic Groups of p-power Order," 4th International Conference on Science, Engineering and Environment (SEE), Nagoya, Japan, Nov.12-14, 2018.

M. K. Shahoodh, M. S. Mohamad, Y. Yusof, S. A. Sulaiman, "Subgraph of Compatible Action Graph for Finite Cyclic Groups of p-power Order," International Conference on Applied an Industrial Mathematics and Statistics, (ICoAIMS), Journal of Physics: Conference series, 2019.

S. A. Sulaiman, "Compatible Pairs of Actions for Finite cyclic 2-groups and the Associated Compatible Action Graph," Ph.D Thesis, University Malaysia Pahang, 2018.

M. S. Mohamad, "Compatibility Conditions and Nonabelian Tensor Products of Finite Cyclic Groups of p-power Order," P.hD Thesis, University Technology Malaysia, 2012.

D. S. Dummit and R. M. Foot, " Abstract algebra," USA. John Wily and Sons, 2004.

J. K. Pahade and M. Jha, "Trace of Positive Integer Power of Adjacency Matrix," Global journal of Pure and Applied Mathematics, vol. 13, no. 6,pp.2079-2087, 2017.

R. J. Wilson, "Introduction to Graph Theory,". 5th Ed, British library, Library of Congress, pp.8-49, 2010.

K. Rosen. "Discrete Mathematics and its Applications," 7th Ed, USA, New York, McGraw-Hill, pp. 641-735, 2012.

Downloads

Published

2024-03-30

Issue

Section

Mathematics

How to Cite

[1]
mohd Shahoodh, “Non-Compatible Action Graph and Its Adjacency Matrix for The Non-abelian Tensor Product for Groups of Prime Power Order”, WJCMS, vol. 3, no. 1, pp. 54–62, Mar. 2024, doi: 10.31185/wjcms.204.