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Click and drag the steps to show that in a simple graph with at least two vertices, there must be two vertices that have the san degree. Step 1 The degree of a vertex, v; has possible values 0, 1, ..., n-1, where n ≥ 2 is the number of vertices in the graph. The degree of each of the n vertices comes from a set of at most n - 1 elements; hence two must not have the same degree. Step 2 The degree of a vertex, vi has possible values 1, 2, 3, ..., n + 1, where n ≥ 2 is the number of vertices in the graph. Step 3 It is impossible for there to be both an i with V; = 0 and a j with v; = n - 1 because if one vertex is connected to every other vertex, then it is still possible for one vertex to be connected to no other vertex. The degree of each of the n vertices comes from a set of at most n - 1 elements and hence at least two must have the same degree. Reset Consider an acquaintanceship graph, where vertices represent all the people in the world. Click and drag the phrases on the right to match with the phrases on the left. The degree of a vertex v is the set of all people whom v knows. the average person knows 1000 other people. The neighborhood of a vertex v is An isolated vertex is A pendant vertex is the number of people v knows. a person who knows more than one other person. a person who knows no one. If the average degree is 1000, then the average person knows 500 other people. a person who knows just one other person. Reset

Click and drag the steps to show that in a simple graph with at least two vertices, there must be two vertices that have the san degree. Step 1 The degree of a vertex, v; has possible values 0, 1, ..., n-1, where n ≥ 2 is the number of vertices in the graph. The degree of each of the n vertices comes from a set of at most n - 1 elements; hence two must not have the same degree. Step 2 The degree of a vertex, vi has possible values 1, 2, 3, ..., n + 1, where n ≥ 2 is the number of vertices in the graph. Step 3 It is impossible for there to be both an i with V; = 0 and a j with v; = n - 1 because if one vertex is connected to every other vertex, then it is still possible for one vertex to be connected to no other vertex. The degree of each of the n vertices comes from a set of at most n - 1 elements and hence at least two must have the same degree. Reset Consider an acquaintanceship graph, where vertices represent all the people in the world. Click and drag the phrases on the right to match with the phrases on the left. The degree of a vertex v is the set of all people whom v knows. the average person knows 1000 other people. The neighborhood of a vertex v is An isolated vertex is A pendant vertex is the number of people v knows. a person who knows more than one other person. a person who knows no one. If the average degree is 1000, then the average person knows 500 other people. a person who knows just one other person. Reset

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter1: Expressions And Functions
Section1.8: Interpreting Graphs Of Functions
Problem 25PFA
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Click and drag the steps to show that in a simple graph with at least two vertices, there must be two vertices that have the san degree. Step 1 The degree of a vertex, v; has possible values 0, 1, ..., n-1, where n ≥ 2 is the number of vertices in the graph. The degree of each of the n vertices comes from a set of at most n - 1 elements; hence two must not have the same degree. Step 2 The degree of a vertex, vi has possible values 1, 2, 3, ..., n + 1, where n ≥ 2 is the number of vertices in the graph. Step 3 It is impossible for there to be both an i with V; = 0 and a j with v; = n - 1 because if one vertex is connected to every other vertex, then it is still possible for one vertex to be connected to no other vertex. The degree of each of the n vertices comes from a set of at most n - 1 elements and hence at least two must have the same degree. Reset
Transcribed Image Text:Click and drag the steps to show that in a simple graph with at least two vertices, there must be two vertices that have the san degree. Step 1 The degree of a vertex, v; has possible values 0, 1, ..., n-1, where n ≥ 2 is the number of vertices in the graph. The degree of each of the n vertices comes from a set of at most n - 1 elements; hence two must not have the same degree. Step 2 The degree of a vertex, vi has possible values 1, 2, 3, ..., n + 1, where n ≥ 2 is the number of vertices in the graph. Step 3 It is impossible for there to be both an i with V; = 0 and a j with v; = n - 1 because if one vertex is connected to every other vertex, then it is still possible for one vertex to be connected to no other vertex. The degree of each of the n vertices comes from a set of at most n - 1 elements and hence at least two must have the same degree. Reset
Consider an acquaintanceship graph, where vertices represent all the people in the world. Click and drag the phrases on the right to match with the phrases on the left. The degree of a vertex v is the set of all people whom v knows. the average person knows 1000 other people. The neighborhood of a vertex v is An isolated vertex is A pendant vertex is the number of people v knows. a person who knows more than one other person. a person who knows no one. If the average degree is 1000, then the average person knows 500 other people. a person who knows just one other person. Reset
Transcribed Image Text:Consider an acquaintanceship graph, where vertices represent all the people in the world. Click and drag the phrases on the right to match with the phrases on the left. The degree of a vertex v is the set of all people whom v knows. the average person knows 1000 other people. The neighborhood of a vertex v is An isolated vertex is A pendant vertex is the number of people v knows. a person who knows more than one other person. a person who knows no one. If the average degree is 1000, then the average person knows 500 other people. a person who knows just one other person. Reset
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