Open AccessThe structure of Cayley graphs of dihedral groups of Valencies 1, 2 and 3
Author(s) -
Saba Al-Kaseasbeh,
Ahmad Erfanian
Publication year - 2021
Publication title -
proyecciones
Language(s) - English
Resource type - Journals
eISSN - 0717-6279
pISSN - 0716-0917
DOI - 10.22199/issn.0717-6279-4357-4429
Subject(s) - valency , dihedral group , cayley graph , combinatorics , mathematics , undirected graph , dihedral angle , cayley's theorem , graph , group (periodic table) , order (exchange) , discrete mathematics , chemistry , voltage graph , hydrogen bond , philosophy , linguistics , organic chemistry , finance , line graph , molecule , economics
Let G be a group and S be a subset of G such that e ∉ S and S−1 ⊆ S. Then Cay(G, S) is a simple undirected Cayley graph whose vertices are all elements of G and two vertices x and y are adjacent if and only if xy−1 ∈ S. The size of subset S is called the valency of Cay(G, S). In this paper, we determined the structure of all Cay(D2n, S), where D2n is a dihedral group of order 2n, n ≥ 3 and |S| = 1, 2 or 3.