Some Special Graphs of Quaternion Group

Abdul Gazir S; I Gede Adhitya Wisnu Wardhana

doi:10.29303/emj.v4i1.74

Authors

Abdul Gazir S
I Gede Adhitya Wisnu Wardhana

DOI:

https://doi.org/10.29303/emj.v4i1.74

Keywords:

quaternion group, special graph, complete graph, regular graph.

Abstract

Research on an algebraic structure represented in graph theory opens the way for new research in recent years. Several types of new graphs continue to be developed, such as coprime and non-coprime graphs. This article will represent the quaternion group in several graphs, such as coprime graphs, non-coprime graphs, commuting graphs, non-commuting graphs, and identity graphs. We obtained several theorems about unique graphs. One of the results is that non-coprime graphs from the quaternion group are complete and regular graphs.

References

Abdollahi, A., Akbari, S., and Maimani, H. (2006). Non-commuting Graph of a Group. Journal of Algebra: 468-492.

Fraleigh, J. B. (2014). A First Course in Abstract Algebra Seventh Edition. United States of America: Pearson Education Limited.

Herstein, I. N. (1975). Topics In Algebra, Second Edition. Prentice-Hall, Inc, United: States of America.

Irawan, Muh.. (2015). Quaternion and it’s properties, Jurnal Matematika Statistika dan Analisis Vol 3 No 1.

Juliana, R., Wardahan, I. G. A. W., Switrayni, N. W., Irwansyah, I. (2020). Coprime Graph Of Integers Modulo N Group And Its Subgroups. Journal of Fundamental Mathematics and Applications (JFMA) 3 (1), 15-18.

Kandasamy, W. B., Smarandache, F. (2009). Group As Graph. Romania: Editura Cuart.

Ma X., H. Wei and L. Yang. (2014). The coprime graph of a group. Int. J. Group Theory. 3(3): 13-23.

Mansoori, F., Erfanian A., and Tolue, B. (2016). Non-coprime Graph of a Finite Group. AIP Conference Proceedings.

Masriani, M., Juliana, R., Syarifudin, A.G., Wardhana, I. G. A. W,, Irwansyah, I., Switrayni, N. W. (2020). Some Result Of Non-Coprime Graph Of Integers Modulo N Group For N A Prime Power. Journal of Fundamental Mathematics and Applications (JFMA) 3(2), 107-111.

Misuki, W. U., Wardhana, I. G. A. W., Switrayni, N. W., Irwansyah, I. (2021). Some Results Of Non-Coprime Graph Of The Dihedral Group D2n For N A Prime Power. AIP Conference Proceedings 2329 (1), 020005.

Munir, Rinaldi. (2010). Matematika Diskrit. Bandung:Informatika Bandung.

Nurhabibah, N., Syarifudin, A. G., Wardhana, I. G. A. W. (2021). Some Results of The Coprime Graph of a Generalized Quaternion Group Q_4n. InPrime: Indonesian Journal of Pure and Applied Mathematics 3 (1), 29-33.

Nawawi, A., Rowley, P. (2012). On Commuting Graph for Element of Order 3 in Symetry Groups. Manchester: The MIMS Secretary.

Romdhini, M. U., Irwansyah.,and Switrayni, N. W. (2016). Struktur Aljabar. Mataram: Universitas Mataram.

Syarifudin, A.G., Nurhabibah, N., Malik, D. P., Wardhana, I. G. A. W (2021). Some characterizatsion of coprime graph of dihedral group D_2n. Journal of Physics: Conference Series 1722 (1), 012051.

Syarifudin, A.G., Wardhana, I. G. A. W (2019). Beberapa Sifat Grup Kompleks dan Grup Quaternion. 3^rd ELPSA Conferences: 48-54.