Cycles in a graph

The total number of Hamiltonian circuits in a complete undirected graph of n vertices will be ____
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If G is a simple graph with n-vertices and n>=3, the condition for G has a Hamiltonian circuit is _________
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The time complexity to find a Eulerian path in a graph of vertex V and edge E is
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Consider a connected multigraph with 8 vertices has an Euler circuit. Which of the following degrees is possible for each vertex so that the graph has an Euler circuit?

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The traveling salesman problem involves n cities with paths connecting the cities. The time taken for traversing through all the cities, without knowing in advance the length of a minimum tour, is
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