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A path in graph $G$, which contains every vertex of $G$ and only once?

  1. Euler circuit
  2. Hamiltonian path
  3. Euler Path
  4. Hamiltonian Circuit
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option B is the answer. Following is the explanation

 

Hamiltonian path, also called a Hamilton path, is a graph path between two vertices of a graph that visits each vertex exactly once. If a Hamiltonian path exists whose endpoints are adjacent, then the resulting graph cycle is called a Hamiltonian cycle (or Hamiltonian cycle)
● An Euler path is a path that uses every edge of a graph exactly once. An Euler circuit is a circuit that uses every edge of a graph exactly once.
● An Euler path starts and ends at different vertices.
● An Euler circuit starts and ends at the same vertex.

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Hamiltonian cycle starting vertex and ending vertex should be same.
1
1
Answer:

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