Book Recommendations : Computational Complexity Theory and Graph problems

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I need recommendations for books which deal with classes of Algorithms(P, NP, NP-C etc). I'm interested in knowing new prooving techniques, proving why an algorithm is NP-C(I recently read about the Vertex cover problem and found it's proof mechanism really interesting, I'd like to learn about various Graph theory problems). I'd appreciate it if you could recommend a book which covers the topics I want, sorry If I'm misusing any terminology, I'm quite new to this field.

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Skiena "Algorithm Design Manual" is a great book for learning techniques, and it also contains all most important algorithms. If you want more rigorous treatment of ideas, get Cormen, Leiserson, Rivest, and Stein "Introduction to Algorithms".