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Explain why it is not possible to draw a planar graph that contains three faces and has the same number of vertices as edges.
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Mathematical Excursions (MindTap C...
4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
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Mathematical Excursions (MindTap C...
4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 5.3, Problem 27ES
Textbook Problem
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Explain why it is not possible to draw a planar graph that contains three faces and has the same number of vertices as edges.
To determine
To explain:
The reason for that it is not possible to draw a planar graph that contains three faces and has the same number of vertices as edges
Explanation of Solution
Given information:
Number of faces (f) = 3
It is not possible to draw a planar graph that contains three faces and has the same number of vertices as edges as because it wouldn't satisfy the Euler's formula.
Consider a graph contains same number of vertices and edges.
Number of vertices (v) = x
Number of edges (c) = x
Then the Euler's formula
Chapter 5 Solutions
Mathematical Excursions (MindTap Course List)
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addCh. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - Explain why the following pen-tracing puzzle is...Ch. 5.1 - Transportation An X in the table below indicates a...Ch. 5.1 - Transportation The table below shows the nonstop...Ch. 5.1 - Social Network A group of friends is represented...Ch. 5.1 - Baseball The local Little League baseball teams...Ch. 5.1 - Determine (a) the number of edges in the graph,...
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