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Graph Reconstruction

Graph Reconstruction Quiz

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

Which of the following is a necessary condition for a graph to be reconstructible?

  1. The degree sequence of the graph is unique.
  2. The number of edges in the graph is even.
  3. The graph is connected.
  4. The graph is a tree.
Question 2 Multiple Choice (Single Answer)

Which of the following is a sufficient condition for a graph to be reconstructible?

  1. The degree sequence of the graph is unique.
  2. The number of edges in the graph is even.
  3. The graph is connected.
  4. The graph is a tree.
Question 3 Multiple Choice (Single Answer)

Which of the following graphs is not reconstructible?

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

Which of the following is a necessary condition for a graph to be uniquely reconstructible?

  1. The degree sequence of the graph is unique.
  2. The number of edges in the graph is even.
  3. The graph is connected.
  4. The graph is a tree.
Question 5 Multiple Choice (Single Answer)

Which of the following is a sufficient condition for a graph to be uniquely reconstructible?

  1. The degree sequence of the graph is unique.
  2. The number of edges in the graph is even.
  3. The graph is connected.
  4. The graph is a tree.
Question 6 Multiple Choice (Single Answer)

Which of the following graphs is uniquely reconstructible?

  1. A path graph
  2. A cycle graph
  3. A complete graph
  4. A star graph
Question 7 Multiple Choice (Single Answer)

Which of the following is a necessary condition for a graph to be reconstructible from its edge degrees?

  1. The edge degrees of the graph are unique.
  2. The number of edges in the graph is even.
  3. The graph is connected.
  4. The graph is a tree.
Question 8 Multiple Choice (Single Answer)

Which of the following is a sufficient condition for a graph to be reconstructible from its edge degrees?

  1. The edge degrees of the graph are unique.
  2. The number of edges in the graph is even.
  3. The graph is connected.
  4. The graph is a tree.
Question 9 Multiple Choice (Single Answer)

Which of the following graphs is not reconstructible from its edge degrees?

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

Which of the following is a necessary condition for a graph to be uniquely reconstructible from its edge degrees?

  1. The edge degrees of the graph are unique.
  2. The number of edges in the graph is even.
  3. The graph is connected.
  4. The graph is a tree.
Question 11 Multiple Choice (Single Answer)

Which of the following is a sufficient condition for a graph to be uniquely reconstructible from its edge degrees?

  1. The edge degrees of the graph are unique.
  2. The number of edges in the graph is even.
  3. The graph is connected.
  4. The graph is a tree.
Question 12 Multiple Choice (Single Answer)

Which of the following graphs is uniquely reconstructible from its edge degrees?

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

Which of the following is a necessary condition for a graph to be reconstructible from its Laplacian spectrum?

  1. The Laplacian spectrum of the graph is unique.
  2. The number of edges in the graph is even.
  3. The graph is connected.
  4. The graph is a tree.
Question 14 Multiple Choice (Single Answer)

Which of the following is a sufficient condition for a graph to be reconstructible from its Laplacian spectrum?

  1. The Laplacian spectrum of the graph is unique.
  2. The number of edges in the graph is even.
  3. The graph is connected.
  4. The graph is a tree.
Question 15 Multiple Choice (Single Answer)

Which of the following graphs is not reconstructible from its Laplacian spectrum?

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