Simulation of the Properties of the Coprime Graph of the Dihedral Group with Prime Order
Abstract
The dihedral group of order 2n denoted by D_2n is the symmetry group of a regular n-polygon consisting of rotation and reflection elements and the composition of both elements. We then construct a coprime graph of the dihedral group with prime order. Many properties can be studied from this coprime graph including the shape, spectrum, tree numbers, chromatic numbers, etc. By utilizing the Python programming language, we can draw this graph and simulate the properties concerning this graph to get more insight on it.
References
X. Ma, H. Wei & L. Yang, The Coprime graph of a Group, International Journal of Group Theory, 3(3), pp. 13-23, 2014.
R. Juliani, M. Masriani, I. G. A. W. Wardhana, N. W. Switrayni & I. Irwansyah, Coprime Graph of Integers Modulo N Group and Its Subgroups, Journal of Fundamental Mathematics and Applications (JFMA), 3(1), pp. 15-18, 2020.
A. G. Syarifudin, N. Nurhabibah, D. P. Malik & I. G. A. W. Wardhana, Some characterizatsion of coprime graph of dihedral group D2n, Journal of Physics: Conference Series, 1722(1), 2021.
A. G. Syarifudin, I. G. A. W. Wardhana, N. W. Switrayni and Q. Aini, Some Properties of Coprime Graph of Dihedral Group D2n When n is prime power, Journal of Physics: Conference Series, 1722(1), 2021.
A. G. Syarifudin, I. G. A. W. Wardhana, N. W. Switrayni and Q. Aini, The Clique Numbers and Chromatic Numbers of the Coprime Graph of a Dihedral Group, IOP Conference Series: Materials Science and Engineering, 1115(1), 2021.
N. Nurhabibah, A. G. Syarifudin and I. G. A. W. Wardhana, Some Results of the Coprime Graph of a Generalized Quaternion Group Q_4n, InPrime: Indonesian Journal of Pure and Applied Mathematics, 3(1), pp. 29-33, 2021.
J. A. Gallian, Contemporary Abstract Algebra 7th Edition, Belmont: Cengage Learning, 2009.
N. Biggs, Algebraic Graph Theory, New York: Cambridge University Press, 1996.
H. P. Langtangen, A Primer on Scientific Programming with Python 5th Edition, Springer Nature, 2016.
I. B. Muktyas & S. Arifin, Semua Subgrup Siklik dari Grup (Zn, +), Jurnal Teorema: Teori dan Riset Matematika, pp. 177-186, 2018.
J. Hamm & A. Way, Parameters of the Coprime Graph of a Group, International Journal of Group Theory, 10(3), 2021.
