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Eulerian and Hamiltonian Graphs

Eulerian and Hamiltonian Graphs Quiz

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

In a connected graph, an Eulerian path is a path that:

  1. Visits every vertex exactly once
  2. Visits every edge exactly once
  3. Visits every vertex at least once
  4. Visits every edge at least once
Question 2 Multiple Choice (Single Answer)

In a connected graph, an Eulerian circuit is a circuit that:

  1. Visits every vertex exactly once
  2. Visits every edge exactly once
  3. Visits every vertex at least once
  4. Visits every edge at least once
Question 3 Multiple Choice (Single Answer)

Which of the following graphs has an Eulerian circuit?

  1. A complete graph
  2. A tree
  3. A cycle
  4. A path
Question 4 Multiple Choice (Single Answer)

Which of the following graphs has an Eulerian path but not an Eulerian circuit?

  1. A complete graph
  2. A tree
  3. A cycle
  4. A path
Question 5 Multiple Choice (Single Answer)

Which of the following graphs does not have an Eulerian path or an Eulerian circuit?

  1. A complete graph
  2. A tree
  3. A cycle
  4. A path
Question 6 Multiple Choice (Single Answer)

In a connected graph, a Hamiltonian path is a path that:

  1. Visits every vertex exactly once
  2. Visits every edge exactly once
  3. Visits every vertex at least once
  4. Visits every edge at least once
Question 7 Multiple Choice (Single Answer)

In a connected graph, a Hamiltonian circuit is a circuit that:

  1. Visits every vertex exactly once
  2. Visits every edge exactly once
  3. Visits every vertex at least once
  4. Visits every edge at least once
Question 8 Multiple Choice (Single Answer)

Which of the following graphs has a Hamiltonian circuit?

  1. A complete graph
  2. A tree
  3. A cycle
  4. A path
Question 9 Multiple Choice (Single Answer)

Which of the following graphs has a Hamiltonian path but not a Hamiltonian circuit?

  1. A complete graph
  2. A tree
  3. A cycle
  4. A path
Question 10 Multiple Choice (Single Answer)

Which of the following graphs does not have a Hamiltonian path or a Hamiltonian circuit?

  1. A complete graph
  2. A tree
  3. A cycle
  4. A path
Question 11 Multiple Choice (Single Answer)

Euler's formula states that for a connected graph with v vertices and e edges, the following equation holds:

  1. v + e = 2
  2. v - e = 2
  3. v + e = f
  4. v - e = f
Question 12 Multiple Choice (Single Answer)

Which of the following graphs has an odd number of vertices?

  1. A complete graph
  2. A tree
  3. A cycle
  4. A path
Question 13 Multiple Choice (Single Answer)

Which of the following graphs has an even number of vertices?

  1. A complete graph
  2. A tree
  3. A cycle
  4. A path
Question 14 Multiple Choice (Single Answer)

Which of the following graphs has an odd number of edges?

  1. A complete graph
  2. A tree
  3. A cycle
  4. A path
Question 15 Multiple Choice (Single Answer)

Which of the following graphs has an even number of edges?

  1. A complete graph
  2. A tree
  3. A cycle
  4. A path
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