Let the degree sequence of a graph G be the sequence of length IV (G)| that contains the degrees of the vertices of G in non-increasing order. Using a simple graph with 9 vertices, such that the degree of each vertex is either 5 or 6. Prove that there are at least 5 vertices of degree 6 or at least 6 vertices of degree 5. Draw the graph, with your proof.
Let the degree sequence of a graph G be the sequence of length IV (G)| that contains the degrees of the vertices of G in non-increasing order. Using a simple graph with 9 vertices, such that the degree of each vertex is either 5 or 6. Prove that there are at least 5 vertices of degree 6 or at least 6 vertices of degree 5. Draw the graph, with your proof.
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 handwrite the solution, draw a clear graph to help understand and show proof. Thanks
Transcribed Image Text:Let the degree sequence of a graph G be the sequence of length IV (G)|
that contains the degrees of the vertices of G in non-increasing order.
Using a simple graph with 9 vertices, such that the degree of each vertex is either 5
or 6. Prove that there are at least 5 vertices of degree 6 or at least 6 vertices of
degree 5.
Draw the graph, with your proof.
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