Could a spanning tree be a Hamiltonian circuit?

We note that a Hamiltonian path is a spanning tree by definition with at most 2 leaves (accounting for the trivial edge cases of the empty graph and the graph on one node). Conversely, a spanning tree with at most 2 leaves is a also Hamiltonian path.

Which of the following algorithm design method can be used to solve the Hamiltonian cycle problem for an undirected graph?

1. Which of the following algorithm can be used to solve the Hamiltonian path problem efficiently? Explanation: The Hamiltonian path problem can be solved efficiently using branch and bound approach. It can also be solved using a backtracking approach.

What is Hamiltonian cycle explain how it can be solved by backtracking algorithm?

Hamiltonian Path in an undirected graph is a path that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a Hamiltonian Path such that there is an edge (in the graph) from the last vertex to the first vertex of the Hamiltonian Path.

Which Hamiltonian circuit gives the minimum weight?

A number added to the edge of a graph is called a weight. A minimum-cost Hamiltonian circuit is one with the lowest possible sum of the weights of its edges. The problem of finding this minimum- cost Hamiltonian circuit is called the traveling salesman problem (TSP).

What is a minimum length Hamiltonian cycle?

Insert a K4 minus an edge into that edge. The new graph has two hamiltonian cycles (shown in red at the bottom left and right) which have hamming distance 2. You can do this for any cubic graph which has a hamiltonian cycle so you can get any number of vertices and still have minimum hamming distance 2.

What is an algorithm design method that can be used where the solution to a problem can be viewed as a result of sequence of decisions?

Dynamic programming is an algorithm design method that can be used when a solution to the problem is viewed as the result of sequence of decisions.

Which of the following is not the algorithm to find the minimum spanning tree of the given graph?

9. Which of the following is not the algorithm to find the minimum spanning tree of the given graph? Explanation: The Boruvka’s algorithm, Prim’s algorithm and Kruskal’s algorithm are the algorithms that can be used to find the minimum spanning tree of the given graph.

Which problem Cannot be solved by backtracking method?

Which of the problems cannot be solved by backtracking method? Explanation: N-queen problem, subset sum problem, Hamiltonian circuit problems can be solved by backtracking method whereas travelling salesman problem is solved by Branch and bound method.