Test On Euler And Hamilton Paths And Circuits

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Test On Euler And Hamilton Paths And Circuits - Quiz

Test your knowledge of Euler and Hamilton Paths and Circuits with this amazing quiz and determine whether a graph has an Euler or a Hamilton path. An Euler path is a path in a graph that uses every edge exactly one time, and it starts and ends at different vertices. A Hamilton path is a path in a graph that uses every vertex exactly once, and it begins and ends at the same vertex. The below quiz is based on Euler and Hamilton paths and/or circuits. Play it now and check your scores. Good luck!


Questions and Answers
  • 1. 
    Use the above graph. The degree of Vertex C is:
  • 2. 
    Refer to the above graph and choose the best answer:
    • A. 

      Euler path and Euler circuit

    • B. 

      Euler path only

    • C. 

      Euler circuit only

    • D. 

      Neither an Euler path nor Euler circuit

  • 3. 
    Refer to the above graph and choose the best answer:
    • A. 

      Hamiltonian path only

    • B. 

      Hamiltonian circuit only

    • C. 

      Hamiltonian path and Hamiltonian circuit

    • D. 

      Neither a Hamiltonian path nor a Hamiltonian circuit

  • 4. 
    Roberta wants to deliver the mail. She begins at the Post Office where she picks up the mail each day, but wants to end close to her home. She only wants to go down each street once. Her home is 5 miles from the Post Office. Which graph would best meet this scenario?
    • A. 

      Euler path

    • B. 

      Euler circuit

    • C. 

      Hamiltonian path

    • D. 

      Hamiltonian circuit

  • 5. 
    List the vertices in the above graph:
    • A. 

      {A,B,C,D,E,F,G,H}

    • B. 

      {A,B,F,G,H}

    • C. 

      {D,E}

    • D. 

      {F,G,H}

  • 6. 
    A city is planning their snow plow route for next winter. They want to begin at the garage, go down each street only once, and end at the garage. Which graph would be best for this scenario?
    • A. 

      Euler circuit

    • B. 

      Euler graph

    • C. 

      Hamiltonian circuit

    • D. 

      Hamiltonian graph

  • 7. 
    Elizabeth is planning a trip. She wants to fly out of Charlotte, visit New York, visit Hollywood, and end up at her parent's home in Dallas. Which graph would be best for this scenario?
    • A. 

      Hamiltonian path

    • B. 

      Hamiltonian circuit

    • C. 

      Euler path

    • D. 

      Euler circuit

  • 8. 
    Bob has to check the stop signs at every intersection in his hometown. He parks his car in the parking lot of the transportation department and needs to end up back at his car. He only wants to check each intersection one time. Which graph would be best for this scenario?
    • A. 

      Hamiltonian circuit

    • B. 

      Hamiltonian path

    • C. 

      Euler path

    • D. 

      Euler circuit

  • 9. 
    Refer to the above graph and choose the best answer:
    • A. 

      Euler path and Euler circuit

    • B. 

      Euler path only

    • C. 

      Euler circuit only

    • D. 

      Neither an Euler path nor Euler circuit

  • 10. 
    Refer to the above graph and choose the best answer:
    • A. 

      Euler path and Euler circuit

    • B. 

      Euler path only

    • C. 

      Euler circuit only

    • D. 

      Neither an Euler path nor an Euler circuit

  • 11. 
    Use the graph above. The degree of vertex A is:
  • 12. 
    Refer to the above graph and choose the best answer:
    • A. 

      Hamiltonian path and Hamiltonian circuit

    • B. 

      Hamiltonian path

    • C. 

      Hamiltonian circuit

    • D. 

      Neither a Hamiltonian path nor Hamiltonian circuit

  • 13. 
    Use the above graph. The degree of Vertex B is:
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