The structure of Cayley graphs of dihedral groups of Valencies 1, 2 and 3.
DOI:
https://doi.org/10.22199/issn.0717-6279-4357-4429Keywords:
Valency, Cayley graph, Dihedral groupAbstract
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.
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Copyright (c) 2021 Saba AL-Kaseasbeh, Ahmad Erfanian
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