Simulations of Cayley graphs of dihedral group

Department of Mathematics, Faculty of Mathematics and Natural Sciences (FMIPA), Universitas Indonesia, Depok 16424, Indonesia

^* Corresponding author: denny@sci.ui.ac.id

Abstract

Let Γ be a finite group with identity element e and let S ⊆ Γ − {e} which is inverse-closed, i.e., S = S⁻¹ := {s⁻¹ : s ∈ S}. An undirected Cayley graph on a group Γ with connection set S, denoted by Cay(Γ, S), is a graph with vertex set Γ and edges xy for all pairs x,y ∈ Γ such that xy⁻¹ ∈ S. The dihedral group of order 2n, denoted by D_2n, is a group generated by two elements a and b subject to the three relations: aⁿ = e, b² = e, and bab⁻¹ = a⁻¹. In this paper, we investigate the Cayley graphs of the dihedral group for some connection sets S satisfying |S| = 1, 2, 3 by doing simulations using Wolfram Mathematica.