1) Vertex Cover:
Definition: - It represents a set of vertex or node in a graph G (V, E), which gives the connectivity of a complete graph
According to the graph G of vertex cover which you have created, the size of Vertex Cover =2
2) Vertex Cover ≤ρ Clique
In a graph G of Vertex Cover, you have N vertices which contain a Vertex Cover K. There must exist of Clique Size of size N-K in its complement.
According to the graph G, you have
You can also create the Clique by complimenting the graph G of Vertex Cover means in simpler form connect the vertices in Vertex Cover graph G through edges where edges don?t exist and remove all the existed edges
You will get the graph G with Clique Size=4
3) Clique ≤ρ Vertex Cover
Here through the Reduction process, you can get the Vertex Cover form Clique by just complimenting the Clique graph G within the polynomial time.
4) Vertex Cover ϵ NP
As you know very well, you can get the Vertex Cover through Clique and to convert the decision-based NP problem into Clique firstly you have to convert into 3CNF and 3CNF into SAT and SAT into CIRCUIT SAT that comes from NP.
Proof of NPC:-