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 (D)</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 (B)</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 (D)</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 (A)</p> Signup and view all the answers

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

<p>Falling dominoes (D)</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 (C)</p> Signup and view all the answers

What does mathematical induction aim to prove?

<p>That a statement is true for every natural number (D)</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 (B)</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 (C)</p> Signup and view all the answers

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

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

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

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

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