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 -