15 Questions
What is one helpful way to represent a graph without multiple edges?
List all the edges of the graph
Which representation specifies the vertices that are adjacent to each vertex of the graph?
Adjacency lists
In a simple graph G = (V, E) with |V| = n, how are the vertices of G listed?
In arbitrary order
What type of graph representation is used when there are no multiple edges?
Adjacency matrices
Which method is used to describe a simple directed graph using lists of vertices adjacent to each vertex?
Use adjacency lists
In a proof by mathematical induction, what does the base case establish?
The truth of the statement for n = 0
In a proof by mathematical induction, what does the induction step prove?
If the statement holds for n = k, then it must also hold for n = k + 1
Which metaphor is commonly used to explain the technique of mathematical induction?
Falling dominoes
What is the purpose of the base case in mathematical induction?
To establish the truth of the statement for a specific starting natural number
What does mathematical induction aim to prove?
That a statement is true for every natural number
What is the purpose of the induction step in mathematical induction?
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
In a proof by mathematical induction, what does the base case establish?
Proves the statement for n = 0 without assuming any knowledge of other cases
What type of graph representation is used when there are no multiple edges?
Simple graph
Which metaphor is commonly used to explain the technique of mathematical induction?
Climbing a ladder
What does mathematical induction aim to prove?
The infinitely many cases P(0), P(1), P(2), P(3),… all hold
Test your knowledge on graph representation, graph models, terminology, special types of graphs, and connectivity. This quiz covers various ways to represent graphs, including adjacency lists, and explores graph isomorphism.
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