Order Structured Graphs of Cyclic Groups and their Classification

Let Γᵒ(G) with G Cₚ, a cyclic group of order $p,$ be an order structured graph. The group Cₚ will be assumed as the vertex set of the graph Γᵒ(G) and an edge between vertices will be built on the basis of a defined relation via order structure. Certain graphical parameters such as independence ratio, clique number, domination number, and separability are discussed. Some characterizations are proposed and proved by incorporating the defined relation. It is further proved that Γᵒ(Cₚ) can never be a hamiltonian graph. Lastly, It is shown that C(Γᵒ(Cₚ)) is isomorphic to $Γᵒ(Cₚ).