Dm: Chapter 4 Euler & Hamilton Paths/circuits

14 Questions | By Kristijohnsen | Last updated: Feb 8, 2019

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Dm: Chapter 4 Euler & Hamilton Paths/circuits

Test on Euler and Hamilton Paths and Circuits.

Questions and Answers

1.

Match the following:
- A. Connected Graph
- A.
- B. Loop
- B.
- C. Multiple Edges
- C.
- D. Isolated Vertex
- D.
- E. Adjacent
- E.
- F. Degree of a Vertex
- F.
- G. Euler Path
- G.
- H. Euler Circuit
- H.
- I. Hamiltonian Path
- I.
- J. Hamiltonian Circuit
- J.
2.

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}
3.

Fill in the blank. Use the graph above. The degree of vertex A is:
4.

Fill in the blank. Use the above graph. The degree of Vertex B is:
5.

Fill in the blank. Use the above graph. The degree of Vertex C is:
6.

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
7.

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
8.

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
9.

Refer to the above graph and choose the best answer:

Discuss
- A.
  
  Hamiltonian path and Hamiltonian circuit
- B.
  
  Hamiltonian path
- C.
  
  Hamiltonian circuit
- D.
  
  Neither a Hamiltonian path nor Hamiltonian circuit
10.

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
11.

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
12.

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
13.

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?

Discuss
- A.
  
  Hamiltonian circuit
- B.
  
  Hamiltonian path
- C.
  
  Euler path
- D.
  
  Euler circuit
14.

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?

Discuss
- A.
  
  Euler path
- B.
  
  Euler circuit
- C.
  
  Hamiltonian path
- D.
  
  Hamiltonian circuit

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