23. If a planar drawing of a graph has 15 edges and 8 vertices, how many faces does the graph have?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Problem 23:**

If a planar drawing of a graph has 15 edges and 8 vertices, how many faces does the graph have?

To solve this, we can use Euler's formula for planar graphs: 

\[ V - E + F = 2 \]

Where:
- \( V \) is the number of vertices
- \( E \) is the number of edges
- \( F \) is the number of faces

Given:
- \( V = 8 \)
- \( E = 15 \)

Substituting these values into the formula:

\[ 8 - 15 + F = 2 \]

\[ F = 2 + 15 - 8 \]

\[ F = 9 \]

Therefore, the graph has 9 faces.
Transcribed Image Text:**Problem 23:** If a planar drawing of a graph has 15 edges and 8 vertices, how many faces does the graph have? To solve this, we can use Euler's formula for planar graphs: \[ V - E + F = 2 \] Where: - \( V \) is the number of vertices - \( E \) is the number of edges - \( F \) is the number of faces Given: - \( V = 8 \) - \( E = 15 \) Substituting these values into the formula: \[ 8 - 15 + F = 2 \] \[ F = 2 + 15 - 8 \] \[ F = 9 \] Therefore, the graph has 9 faces.
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