Simulation of the Properties of Noncoprime Graph of Finite Group
Verrel Rievaldo Wijaya (*), Abdul Gazir Syarifudin

Department of Mathematics, Bandung Institute of Technology, Bandung 40132, Indonesia
*20121005[at]mahasiswa.itb.ac.id

Abstract

In this paper, we consider some kind of finite groups such as dihedral and generalized quaternion group. 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. Another group that has a similar structure to dihedral group because of its highly related presentations is called generalized quaternion group \( Q_{4n} \). We then construct a noncoprime graph of these two groups, that is the graph where two elements are connected if the order of that elements is not coprime to each other. Many properties can be studied from this graph such as shape, spectrum, 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.

Keywords: noncoprime graph, dihedral group, generalized quaternion group, python, networkx

Topic: MATHEMATICS AND STATISTICS