Question

Do i need to study P, NP computational problems like vertex cover problem also for gate 2015 or only the basic definitions?

Answer 1

You would need to know some examples (not all) of NP Complete problems and why they are NP Complete. For example 3SAT problem is NPC and in GATE they have asked about 2SAT. So, just learning some examples won't be enough.

Answer 2

Yes you need to study P, NP computational problems