# Aptitude | GATE-CS-2015 | Question 2

Consider the following two problems of graph.

**1)** Given a graph, find if the graph has a cycle that visits every vertex exactly once except the first visited vertex which must be visited again to complete the cycle.

**2)** Given a graph, find if the graph has a cycle that visits every edge exactly once.

Which of the following is true about above two problems.

**(A)** Problem 1 belongs NP Complete set and 2 belongs to P**(B)** Problem 1 belongs to P set and 2 belongs to NP Complete set**(C)** Both problems belong to P set**(D)** Both problems belong to NP complete set**Answer:** **(A)****Explanation:** Problem 1 is Hamiltonian Cycle problem which is a famous NP Complete problem.

Problem 2 is Euler Circuit problem which is solvable in Polynomial time.

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