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Paths and Circuits

This quiz is designed to assess your understanding of paths and circuits in graph theory.

13 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

In a graph, a path is a sequence of vertices such that each vertex is connected to the next by an edge. If the last vertex is connected to the first vertex, then the path is called a circuit.

  1. True
  2. False
Question 2 Multiple Choice (Single Answer)

Which of the following is a path in the graph below?

A -- B -- C -- D -- E

  1. A-B-C-D-E
  2. A-B-C-E
  3. A-B-D-E
  4. A-C-D-E
Question 3 Multiple Choice (Single Answer)

Which of the following is a circuit in the graph below?

A -- B -- C -- D -- E
F -- G -- H

  1. A-B-C-D-E-A
  2. F-G-H-F
  3. A-B-C-D-E-F-G-H-A
  4. B-C-D-E-F-G-H-B
Question 4 Multiple Choice (Single Answer)

A graph is called a connected graph if there is a path between every pair of vertices. Which of the following graphs is connected?

A -- B -- C
D -- E -- F

  1. Graph 1
  2. Graph 2
  3. Both
  4. Neither
Question 5 Multiple Choice (Single Answer)

A graph is called a tree if it is connected and has no cycles. Which of the following graphs is a tree?

A -- B -- C
D -- E -- F

  1. Graph 1
  2. Graph 2
  3. Both
  4. Neither
Question 6 Multiple Choice (Single Answer)

In a graph, a spanning tree is a tree that includes all the vertices of the graph. Which of the following graphs is a spanning tree of the graph below?

A -- B -- C
D -- E -- F

  1. Graph 1
  2. Graph 2
  3. Both
  4. Neither
Question 7 Multiple Choice (Single Answer)

In a graph, a Hamiltonian path is a path that visits every vertex exactly once. Which of the following graphs has a Hamiltonian path?

A -- B -- C
D -- E -- F

  1. Graph 1
  2. Graph 2
  3. Both
  4. Neither
Question 8 Multiple Choice (Single Answer)

In a graph, a Eulerian circuit is a circuit that visits every edge exactly once. Which of the following graphs has an Eulerian circuit?

A -- B -- C
D -- E -- F

  1. Graph 1
  2. Graph 2
  3. Both
  4. Neither
Question 9 Multiple Choice (Single Answer)

Which of the following statements is true about a graph with $n$ vertices and $m$ edges?

A. If $m > n$, then the graph must have a circuit.
B. If $m < n$, then the graph must be a tree.
C. If $m = n$, then the graph must be a connected graph.

  1. A only
  2. B only
  3. C only
  4. A and C
Question 10 Multiple Choice (Single Answer)

Which of the following statements is true about a tree with $n$ vertices?

A. A tree with $n$ vertices has $n-1$ edges.
B. A tree with $n$ vertices has $n+1$ edges.
C. A tree with $n$ vertices has $2n-2$ edges.

  1. A only
  2. B only
  3. C only
  4. A and C
Question 11 Multiple Choice (Single Answer)

Which of the following statements is true about a graph with $n$ vertices and $m$ edges?

A. If $m < n-1$, then the graph must be a tree.
B. If $m > n-1$, then the graph must have a circuit.
C. If $m = n-1$, then the graph must be a connected graph.

  1. A only
  2. B only
  3. C only
  4. A and C
Question 12 Multiple Choice (Single Answer)

Which of the following statements is true about a Hamiltonian path in a graph?

A. A Hamiltonian path must visit every vertex exactly once.
B. A Hamiltonian path must visit every edge exactly once.
C. A Hamiltonian path must start and end at the same vertex.

  1. A only
  2. B only
  3. C only
  4. A and C
Question 13 Multiple Choice (Single Answer)

Which of the following statements is true about an Eulerian circuit in a graph?

A. An Eulerian circuit must visit every vertex exactly once.
B. An Eulerian circuit must visit every edge exactly once.
C. An Eulerian circuit must start and end at the same vertex.

  1. A only
  2. B only
  3. C only
  4. A and C
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