TY - GEN

T1 - Simulations of Cayley graphs of dihedral group

AU - Farhan, Mohammad

AU - John, Peter

AU - Silaban, Denny riama

A2 - Aldila, D.

A2 - Zainal abidin, Z.

A2 - Imran, M.

A2 - Widakdo, J.

PY - 2024/1/1

Y1 - 2024/1/1

N2 - 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 D2n, 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.

AB - 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 D2n, 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.

KW - Cayley graph

KW - dihedral group

KW - simulation

UR - https://www.itm-conferences.org/10.1051/itmconf/20246101003

U2 - 10.1051/itmconf/20246101003

DO - 10.1051/itmconf/20246101003

M3 - Conference contribution

VL - 61

T3 - ITM Web of Conferences

BT - The 9th International Symposium on Current Progress in Mathematics and Sciences 2023 (The 9th ISCPMS 2023) in conjunction with AUA Academic Conference on the Application of Artificial Intelligences and Data Sciences in a Modern Science for a Better Life

ER -