Home › Quizzes › Connectivity

Connectivity

Test your understanding of Connectivity in Graph Theory with these challenging questions.

15 Questions Published
Play Quiz Practise this topic out loud

Questions

Question 1 Multiple Choice (Single Answer)

In a connected graph, if a vertex is removed, the resulting graph is:

  1. Always connected
  2. Always disconnected
  3. Sometimes connected and sometimes disconnected
  4. None of the above
Question 2 Multiple Choice (Single Answer)

A graph is said to be Eulerian if:

  1. It has an Eulerian path
  2. It has an Eulerian circuit
  3. It has both an Eulerian path and an Eulerian circuit
  4. None of the above
Question 3 Multiple Choice (Single Answer)

A graph is said to be Hamiltonian if:

  1. It has a Hamiltonian path
  2. It has a Hamiltonian circuit
  3. It has both a Hamiltonian path and a Hamiltonian circuit
  4. None of the above
Question 4 Multiple Choice (Single Answer)

Which of the following statements is true about a connected graph?

  1. It has at least one cycle
  2. It has at least one path between any two vertices
  3. It has a unique Eulerian circuit
  4. All of the above
Question 5 Multiple Choice (Single Answer)

Which of the following statements is true about a tree?

  1. It is a connected graph
  2. It has no cycles
  3. It has a unique Eulerian path
  4. All of the above
Question 6 Multiple Choice (Single Answer)

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

  1. It is an edge whose removal increases the number of connected components in the graph
  2. It is an edge whose removal decreases the number of connected components in the graph
  3. It is an edge whose removal does not change the number of connected components in the graph
  4. None of the above
Question 7 Multiple Choice (Single Answer)

Which of the following statements is true about a cut vertex in a graph?

  1. It is a vertex whose removal increases the number of connected components in the graph
  2. It is a vertex whose removal decreases the number of connected components in the graph
  3. It is a vertex whose removal does not change the number of connected components in the graph
  4. None of the above
Question 8 Multiple Choice (Single Answer)

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

  1. It is a maximal connected subgraph
  2. It is a minimal connected subgraph
  3. It is a subgraph that contains all the cycles in the graph
  4. None of the above
Question 9 Multiple Choice (Single Answer)

Which of the following statements is true about a 2-connected graph?

  1. It has at least two paths between any two vertices
  2. It has at least two cycles
  3. It has a unique Eulerian circuit
  4. All of the above
Question 10 Multiple Choice (Single Answer)

Which of the following statements is true about a k-connected graph?

  1. It has at least k paths between any two vertices
  2. It has at least k cycles
  3. It has a unique Eulerian circuit
  4. All of the above
Question 11 Multiple Choice (Single Answer)

Which of the following statements is true about a planar graph?

  1. It can be drawn on a plane without any edge crossings
  2. It has a unique Eulerian circuit
  3. It is always a tree
  4. None of the above
Question 12 Multiple Choice (Single Answer)

Which of the following statements is true about a Kuratowski graph?

  1. It is a planar graph
  2. It is a non-planar graph
  3. It is a graph that contains a cycle of length 5
  4. None of the above
Question 13 Multiple Choice (Single Answer)

Which of the following statements is true about a Petersen graph?

  1. It is a planar graph
  2. It is a non-planar graph
  3. It is a graph that contains a cycle of length 5
  4. All of the above
Question 14 Multiple Choice (Single Answer)

Which of the following statements is true about a Tutte graph?

  1. It is a planar graph
  2. It is a non-planar graph
  3. It is a graph that contains a cycle of length 5
  4. None of the above
Question 15 Multiple Choice (Single Answer)

Which of the following statements is true about a Heawood graph?

  1. It is a planar graph
  2. It is a non-planar graph
  3. It is a graph that contains a cycle of length 5
  4. None of the above
← Back to Quizzes