## Vertex Cover- Vertex Cover Definition
- Vertex Cover ≤ρ Clique
- Clique ≤ρ Vertex Cover
- Vertex Cover ϵ NP
## 1) Vertex Cover:
According to the graph G of vertex cover which you have created, ## 2) Vertex Cover ≤ρ CliqueIn 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.
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 CoverHere 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 NPAs 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.
- Reduction from Clique to Vertex Cover has been made within the polynomial time. In the simpler form, you can convert into Vertex Cover from Clique within the polynomial time
- And verification has also been done when you convert Vertex Cover to Clique and Clique to 3CNF and satisfy/verified the output within a polynomial time also, so it concluded that Reduction and Verification had been done in the polynomial time that means
**Vertex Cover also comes in NPC**
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