The Cyclic and Normal Graphs of the Group D2n Cp, where p is an Odd Prime

Suppose G is a group. The cyclic graph ????CG is a simple graph with vertex set G and the edge set E(????C(G)) = ffx; yg j ⟨x; y⟩ C Gg, where ⟨x; y⟩ C G means that ⟨x; y⟩ is a cyclic subgroup of G: The normal graph ????NG is anther graph with the same set of vertices and the edge set E(????N(G)) = ffx; yg j ⟨x; y⟩ Gg. In this paper, we establish some properties of the cyclic and normal graphs de ned on the group D2n Cp, where p is an odd prime.