Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)

3rd Edition

ISBN: 9780134689555

Author: Edgar Goodaire, Michael Parmenter

Publisher: PEARSON

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Chapter 9.3, Problem 8E

[BB] Prove that two graphs that are isomorphic must contain the same number of triangles.
Prove that, for any n ≥ 4 , two isomorphic graphs must contain the same number of n- cycles.
How many edges are there in the graphs G 1 and G 2 ? How many vertices? What is the degree sequence of each graph? Are the graphs isomorphic? Explain.

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Chapter 9.3, Problem 7E

Chapter 9.3, Problem 9E

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Chapter 9 Solutions

Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)

Ch. 9.1 - (Answers can be found in the back of the book.) 1....Ch. 9.1 - (Answers can be found in the back of the book.) 2....Ch. 9.1 - (Answers can be found in the back of the book.)...Ch. 9.1 - (Answers can be found in the back of the book.)...Ch. 9.1 - (Answers can be found in the back of the book.) 5....Ch. 9.1 - Prob. 6TFQ Ch. 9.1 - Prob. 7TFQ Ch. 9.1 - Prob. 8TFQ Ch. 9.1 - Prob. 9TFQ Ch. 9.1 - Prob. 10TFQ

Ch. 9.1 - 1. [BB](Fictitious) A recently discovered map of...Ch. 9.1 - Prob. 2E Ch. 9.1 - 3. One of the owners of the houses in the Three...Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - You and a friend meet three other couples at a...Ch. 9.1 - 8. (a) A graph has six vertices, every two of...Ch. 9.1 - [BB] A graph has six vertices, every two of which...Ch. 9.1 - Prob. 10E Ch. 9.1 - Prob. 11E Ch. 9.2 - Prob. 1TFQ Ch. 9.2 - Prob. 2TFQ Ch. 9.2 - Prob. 3TFQ Ch. 9.2 - (Answers can be found in the back of the book.) is...Ch. 9.2 - Prob. 5TFQ Ch. 9.2 - Prob. 6TFQ Ch. 9.2 - Prob. 7TFQ Ch. 9.2 - Prob. 8TFQ Ch. 9.2 - Prob. 9TFQ Ch. 9.2 - Prob. 10TFQ Ch. 9.2 - Prob. 1E Ch. 9.2 - Prob. 2E Ch. 9.2 - Prob. 3E Ch. 9.2 - Prob. 4E Ch. 9.2 - Prob. 5E Ch. 9.2 - Prob. 6E Ch. 9.2 - Prob. 7E Ch. 9.2 - Draw a graph with 64 vertices representing the...Ch. 9.2 - Consider again the graph accompanying Exercise 5...Ch. 9.2 - Prob. 10E Ch. 9.2 - Prob. 11E Ch. 9.2 - Prob. 12E Ch. 9.2 - 13. [BB] At most social functions, there is a lot...Ch. 9.2 - Prob. 14E Ch. 9.2 - 15. [BB;(a)] for each pair of graphs shown,...Ch. 9.2 - Prob. 16E Ch. 9.2 - Prob. 17E Ch. 9.2 - For each of the following sequences, determine if...Ch. 9.2 - Prob. 19E Ch. 9.2 - [BB] A graph has five vertices of degree 4 and two...Ch. 9.2 - Determine whether each of the graphs in Fig 9.23...Ch. 9.2 - Prob. 22E Ch. 9.2 - Prob. 23E Ch. 9.2 - 24. [BB](requires calculus) Prove that the number...Ch. 9.2 - Prob. 25E Ch. 9.2 - Prob. 26E Ch. 9.2 - Prob. 27E Ch. 9.2 - Prob. 28E Ch. 9.2 - Prob. 29E Ch. 9.2 - Prob. 30E Ch. 9.2 - Prob. 31E Ch. 9.2 - Prob. 32E Ch. 9.2 - Prob. 33E Ch. 9.2 - Prob. 34E Ch. 9.2 - Prob. 35E Ch. 9.3 - (Answers can be found in the back of the book.) It...Ch. 9.3 - Prob. 2TFQ Ch. 9.3 - Prob. 3TFQ Ch. 9.3 - Prob. 4TFQ Ch. 9.3 - Prob. 5TFQ Ch. 9.3 - (Answers can be found in the back of the book.) 6....Ch. 9.3 - (Answers can be found in the back of the book.) If...Ch. 9.3 - Prob. 8TFQ Ch. 9.3 - Prob. 9TFQ Ch. 9.3 - Prob. 10TFQ Ch. 9.3 - [BB] For each of the ten pairs of graphs that can...Ch. 9.3 - Prob. 2E Ch. 9.3 - [BB] Draw all nonisomorphic graphs on n =3...Ch. 9.3 - [BB;(b)] for each pair of grpahs shown. If the...Ch. 9.3 - Prob. 5E Ch. 9.3 - Prob. 6E Ch. 9.3 - Prob. 7E Ch. 9.3 - [BB] Prove that two graphs that are isomorphic...Ch. 9.3 - Consider the following three graphs. [BB] How many...Ch. 9.3 - Prob. 10E Ch. 9.3 - Prob. 11E Ch. 9 - 1. In the Konigsberg Bridge Problem, a tragic fire...Ch. 9 - 2. (a) Draw a configuration of four houses and two...Ch. 9 - 3. Find the solutions, where possible, for the...Ch. 9 - Draw a graph with six vertices at least three of...Ch. 9 - For each of the following sequences, determine if...Ch. 9 - 6. (a) Does there exist a graph with degree...Ch. 9 - Determine whether or not each of the following...Ch. 9 - Answer these questions for each sequence: Does...Ch. 9 - Find a necessary and sufficient condition for the...Ch. 9 - Prob. 10RE Ch. 9 - Suppose a graph has 49 vertices, each of degree 4...Ch. 9 - Prob. 12RE Ch. 9 - A graph G has 50 edges, four vertices of degree 2,...Ch. 9 - Prob. 14RE Ch. 9 - For each pair of graphs shown in fig 9.30 If the...Ch. 9 - Prob. 16RE Ch. 9 - 17. For each of the following cases, explain why...Ch. 9 - George is examining three graphs G1, G2, G3. He...Ch. 9 - Answer Exercise 18 again, assuming that Georges...Ch. 9 - Prob. 20RE

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Solution Summary: The author explains that two isomorphic graphs must contain the same number of triangles. The degree sequence of a graph is the degree of the listed order decreasing numerical order.

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Chapter 9 Solutions