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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In a weighted graph G, what is the time complexity of finding both an Euler circuit and a minimum spanning tree?
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What is the maximum number of edges possible in a planar graph with n vertices (n ≥ 3) that has no triangular faces?
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In a tournament graph with n vertices, what is the minimum number of edges that must be reversed to make the graph strongly connected?
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In a graph G with n vertices, if the sum of degrees of any two non-adjacent vertices is at least n, then G must contain a:
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Given a connected graph G with n vertices and n edges, which of the following must be true?
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In a 3-regular connected graph G with 8 vertices, how many different perfect matchings are possible?

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