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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Textbook Question

Chapter 12.4, Problem 5E

The algorithm described in the proof of theorem 12.4.3 can in fact be adapted to find a cycle in a diagraph that is not acyclic.

Explain how this can be accomplished.
Describe an algorithm that implements your idea.
Write computer code that implements your algorithm.

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Chapter 12.4, Problem 4E

Chapter 12.4, Problem 6E

Chapter 12 Solutions

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

Ch. 12.1 - Prob. 1TFQ Ch. 12.1 - Prob. 2TFQ Ch. 12.1 - Prob. 3TFQ Ch. 12.1 - Prob. 4TFQ Ch. 12.1 - Prob. 5TFQ Ch. 12.1 - Prob. 6TFQ Ch. 12.1 - Prob. 7TFQ Ch. 12.1 - Prob. 8TFQ Ch. 12.1 - Prob. 9TFQ Ch. 12.1 - Prob. 10TFQ

Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - Prob. 7E Ch. 12.1 - Prob. 8E Ch. 12.1 - 9. The vertices in the graph represent town; the...Ch. 12.1 - Prob. 11E Ch. 12.1 - 12. [BB] suppose and are two paths from a vertex...Ch. 12.1 - Prob. 13E Ch. 12.1 - Prob. 14E Ch. 12.1 - Prob. 15E Ch. 12.1 - Prob. 16E Ch. 12.1 - 17. [BB] Recall that a graph is acyclic if it has...Ch. 12.1 - Prob. 18E Ch. 12.1 - Prob. 19E Ch. 12.1 - Prob. 20E Ch. 12.1 - Prob. 21E Ch. 12.1 - Prob. 22E Ch. 12.1 - The answers to exercises marked [BB] can be found...Ch. 12.1 - Prob. 24E Ch. 12.1 - Prob. 25E Ch. 12.1 - A forest is a graph every component of which is a...Ch. 12.1 - Prob. 27E Ch. 12.2 - Prob. 1TFQ Ch. 12.2 - Prob. 2TFQ Ch. 12.2 - Prob. 3TFQ Ch. 12.2 - Prob. 4TFQ Ch. 12.2 - Prob. 5TFQ Ch. 12.2 - Prob. 6TFQ Ch. 12.2 - Prob. 7TFQ Ch. 12.2 - Prob. 8TFQ Ch. 12.2 - Prob. 9TFQ Ch. 12.2 - Prob. 1E Ch. 12.2 - Prob. 2E Ch. 12.2 - Prob. 3E Ch. 12.2 - Prob. 4E Ch. 12.2 - Prob. 5E Ch. 12.2 - Prob. 6E Ch. 12.2 - Prob. 7E Ch. 12.2 - Prob. 8E Ch. 12.2 - Prob. 9E Ch. 12.2 - Prob. 10E Ch. 12.2 - Prob. 11E Ch. 12.2 - Prob. 12E Ch. 12.2 - Prob. 13E Ch. 12.2 - Prob. 14E Ch. 12.2 - Prob. 15E Ch. 12.2 - Prob. 16E Ch. 12.2 - Prob. 17E Ch. 12.3 - If Kruskal’s algorithm is applied to after one...Ch. 12.3 - 2. If Kruskal’s algorithm is applied to we might...Ch. 12.3 - 3. If Kruskal’s algorithm is applied to we might...Ch. 12.3 - If Prim’s algorithm is applied to after one...Ch. 12.3 - If Prims algorithm is applied to we might end up...Ch. 12.3 - If Prims algorithm is applied to we might end up...Ch. 12.3 - Prob. 7TFQ Ch. 12.3 - Prob. 8TFQ Ch. 12.3 - Prob. 9TFQ Ch. 12.3 - Prob. 10TFQ Ch. 12.3 - Prob. 1E Ch. 12.3 - Prob. 2E Ch. 12.3 - Prob. 3E Ch. 12.3 - Prob. 4E Ch. 12.3 - The answers to exercises marked [BB] can be found...Ch. 12.3 - Prob. 6E Ch. 12.3 - Prob. 7E Ch. 12.3 - Prob. 8E Ch. 12.3 - Prob. 9E Ch. 12.3 - Prob. 10E Ch. 12.3 - Prob. 11E Ch. 12.3 - In our discussion of the complexity of Kruskals...Ch. 12.3 - Prob. 13E Ch. 12.3 - Prob. 14E Ch. 12.3 - Prob. 15E Ch. 12.3 - Prob. 16E Ch. 12.3 - Prob. 17E Ch. 12.3 - Prob. 18E Ch. 12.4 - The digraph pictured by is a cyclic.Ch. 12.4 - Prob. 2TFQ Ch. 12.4 - Prob. 3TFQ Ch. 12.4 - Prob. 4TFQ Ch. 12.4 - Prob. 5TFQ Ch. 12.4 - Prob. 6TFQ Ch. 12.4 - Prob. 7TFQ Ch. 12.4 - Prob. 8TFQ Ch. 12.4 - Prob. 9TFQ Ch. 12.4 - Prob. 10TFQ Ch. 12.4 - Prob. 1E Ch. 12.4 - Prob. 2E Ch. 12.4 - Prob. 3E Ch. 12.4 - Prob. 4E Ch. 12.4 - 5. The algorithm described in the proof of...Ch. 12.4 - How many shortest path algorithms can you name?...Ch. 12.4 - Prob. 7E Ch. 12.4 - Prob. 8E Ch. 12.4 - Prob. 10E Ch. 12.4 - Prob. 11E Ch. 12.4 - Prob. 12E Ch. 12.4 - [BB] Explain how Bellmans algorithm can be...Ch. 12.4 - Prob. 14E Ch. 12.5 - Prob. 1TFQ Ch. 12.5 - Depth-first search has assigned labels 1 and 2 as...Ch. 12.5 - Depth-first search has assigned labels 1 and 2 as...Ch. 12.5 - Prob. 4TFQ Ch. 12.5 - Prob. 5TFQ Ch. 12.5 - Prob. 6TFQ Ch. 12.5 - Prob. 7TFQ Ch. 12.5 - Prob. 8TFQ Ch. 12.5 - 9. Breadth-first search (see exercise 10) has...Ch. 12.5 - Prob. 10TFQ Ch. 12.5 - Prob. 1E Ch. 12.5 - Prob. 2E Ch. 12.5 - Prob. 3E Ch. 12.5 - 4. (a) [BB] Let v be a vertex in a graph G that is...Ch. 12.5 - Prob. 5E Ch. 12.5 - Prob. 6E Ch. 12.5 - Prob. 7E Ch. 12.5 - Prob. 8E Ch. 12.5 - Prob. 9E Ch. 12.5 - Prob. 10E Ch. 12.5 - [BB; (a)] Apply a breath-first search to each of...Ch. 12.5 - Prob. 12E Ch. 12.5 - Prob. 13E Ch. 12.5 - Prob. 14E Ch. 12.6 - Prob. 1TFQ Ch. 12.6 - Prob. 2TFQ Ch. 12.6 - Prob. 3TFQ Ch. 12.6 - Prob. 4TFQ Ch. 12.6 - Prob. 5TFQ Ch. 12.6 - Prob. 6TFQ Ch. 12.6 - Prob. 7TFQ Ch. 12.6 - Prob. 8TFQ Ch. 12.6 - Prob. 9TFQ Ch. 12.6 - Prob. 10TFQ Ch. 12.6 - Prob. 1E Ch. 12.6 - Prob. 2E Ch. 12.6 - Prob. 3E Ch. 12.6 - Prob. 4E Ch. 12.6 - Prob. 5E Ch. 12.6 - Prob. 6E Ch. 12.6 - Prob. 7E Ch. 12.6 - Prob. 8E Ch. 12.6 - Prob. 9E Ch. 12.6 - Prob. 10E Ch. 12.6 - Prob. 11E Ch. 12.6 - Prob. 12E Ch. 12.6 - Prob. 13E Ch. 12.6 - Prob. 14E Ch. 12.6 - Prob. 15E Ch. 12 - Prob. 1RE Ch. 12 - Prob. 2RE Ch. 12 - Prob. 3RE Ch. 12 - Prob. 4RE Ch. 12 - 5. (a) Let G be a graph with the property that...Ch. 12 - Prob. 6RE Ch. 12 - Prob. 7RE Ch. 12 - Prob. 8RE Ch. 12 - Prob. 9RE Ch. 12 - Prob. 10RE Ch. 12 - Prob. 11RE Ch. 12 - Prob. 12RE Ch. 12 - Prob. 13RE Ch. 12 - Prob. 14RE Ch. 12 - Prob. 15RE Ch. 12 - Prob. 16RE Ch. 12 - Prob. 17RE Ch. 12 - Prob. 18RE Ch. 12 - In each of the following graphs, a depth-first...Ch. 12 - Prob. 20RE Ch. 12 - Prob. 21RE Ch. 12 - Prob. 22RE Ch. 12 - Prob. 23RE Ch. 12 - Prob. 24RE Ch. 12 - Prob. 25RE Ch. 12 - Prob. 26RE

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The algorithm described in the proof of theorem 12.4.3 can in fact be adapted to find a cycle in a diagraph that is not acyclic. Explain how this can be accomplished. Describe an algorithm that implements your idea. Write computer code that implements your algorithm.

Solution Summary: The author explains how the algorithm described in the proof of theorem 12.4.3 can be adapted to find a cyclic diagraph.

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Chapter 12 Solutions