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 graphwith 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 normalgraph ????ng is anther graph with the same set of vertices and the edge sete(????n(g)) = ffx; yg j ⟨x; y⟩gg. in this paper, we establish some propertiesof the cyclic and normal graphs dened on the group d2n  cp, where p isan odd prime.