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Graph theory is a well explored, but still expanding area of mathematics and computer science. Efficient algorithms for graph theoretic problems are of immense practical importance. There are numerous problems in graph theory that are NP-complete, i.e., no efficient algorithms can solve them in polynomial times. Genetic algorithms (GAs) are heuristic search and optimization technique where the search methods mimic some natural phenomena: genetic inheritance and survival of the fittest. In this work, GAs are applied successfully on some well-known NP-complete graph theoretic problems. Some other problems in fuzzy environments are also considered here.