Graph Representation and Connectivity Quiz
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Questions and Answers

What is one helpful way to represent a graph without multiple edges?

  • Use adjacency matrices
  • List all the edges of the graph (correct)
  • Use incidence matrices
  • Use adjacency lists

    • Which representation specifies the vertices that are adjacent to each vertex of the graph?

  • Adjacency matrices
  • Listing all the edges of the graph
  • Incidence matrices
  • Adjacency lists (correct)

    • In a simple graph G = (V, E) with |V| = n, how are the vertices of G listed?

  • In alphabetical order
  • In ascending order
  • In descending order
  • In arbitrary order (correct)

    • What type of graph representation is used when there are no multiple edges?

    <p>Adjacency matrices</p> Signup and view all the answers

    Which method is used to describe a simple directed graph using lists of vertices adjacent to each vertex?

    <p>Use adjacency lists</p> Signup and view all the answers

    In a proof by mathematical induction, what does the base case establish?

    <p>The truth of the statement for n = 0</p> Signup and view all the answers

    In a proof by mathematical induction, what does the induction step prove?

    <p>If the statement holds for n = k, then it must also hold for n = k + 1</p> Signup and view all the answers

    Which metaphor is commonly used to explain the technique of mathematical induction?

    <p>Falling dominoes</p> Signup and view all the answers

    What is the purpose of the base case in mathematical induction?

    <p>To establish the truth of the statement for a specific starting natural number</p> Signup and view all the answers

    What does mathematical induction aim to prove?

    <p>That a statement is true for every natural number</p> Signup and view all the answers

    What is the purpose of the induction step in mathematical induction?

    <p>To prove that if the statement holds for any given case n = k, then it must also hold for the next case n = k + 1</p> Signup and view all the answers

    In a proof by mathematical induction, what does the base case establish?

    <p>Proves the statement for n = 0 without assuming any knowledge of other cases</p> Signup and view all the answers

    What type of graph representation is used when there are no multiple edges?

    <p>Simple graph</p> Signup and view all the answers

    Which metaphor is commonly used to explain the technique of mathematical induction?

    <p>Climbing a ladder</p> Signup and view all the answers

    What does mathematical induction aim to prove?

    <p>The infinitely many cases P(0), P(1), P(2), P(3),… all hold</p> Signup and view all the answers

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