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If we form a graph by a projection of the dodecahedron in Figure 5.20, what will the degree of each vertex be? The dodecahedron has 12 faces, each of which has 5 edges. Use this information to determine the number of edges in the projected graph. Use Euler's formula to determine the number of vertices in the projected graph, and hence in the dodecahedron.

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Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

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Chapter
Section
BuyFindarrow_forward

Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 5.3, Problem 3EE
Textbook Problem
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  1. If we form a graph by a projection of the dodecahedron in Figure 5.20, what will the degree of each vertex be?
  2. The dodecahedron has 12 faces, each of which has 5 edges. Use this information to determine the number of edges in the projected graph.
  3. Use Euler's formula to determine the number of vertices in the projected graph, and hence in the dodecahedron.

To determine

(a)

The degree of the vertex of Dodecahedron.

Explanation of Solution

Given information:

The dodecahedron has12 faces, each of which has 5 edges.

Solution:

The graph od Dodecahedron is

To determine

(b)

The number of edges of Dodecahedron.

To determine

(c)

The number of vertices in the Dodecahedron.

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Chapter 5 Solutions

Mathematical Excursions (MindTap Course List)
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Ch. 5.1 - Determine (a) the number of edges in the graph,...Ch. 5.1 - Determine (a) the number of edges in the graph,...Ch. 5.1 - Determine (a) the number of edges in the graph,...Ch. 5.1 - Determine whether the two graphs are equivalent.Ch. 5.1 - Determine whether the two graphs are equivalent.Ch. 5.1 - Determine whether the two graphs are equivalent.Ch. 5.1 - Determine whether the two graphs are equivalent.Ch. 5.1 - Explain why the following two graphs cannot be...Ch. 5.1 - Label the vertices of the second graph so that it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. 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