The structure of Cayley graphs of dihedral groups of Valencies 1, 2 and 3.

• AL-Kaseasbeh, Saba ; Erfanian, Ahmad ^[1]
  1. [1] Ferdowsi University of Mashhad

     Ferdowsi University of Mashhad

     Irán

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 40, Nº. 6, 2021, págs. 1683-1691
• Idioma: inglés
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• Resumen

  • 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.