Simulations of Cayley graphs of dihedral group
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 di...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2024-01-01
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| Series: | ITM Web of Conferences |
| Subjects: | |
| Online Access: | https://www.itm-conferences.org/articles/itmconf/pdf/2024/04/itmconf_iscpms2024_01003.pdf |
| Summary: | 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. |
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| ISSN: | 2271-2097 |