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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help me with these questions. I am having trouble understanding what to do
Thank you
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
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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