If a planar drawing of a graph has twice as many edges as vertices, find a relationship between the number of faces and the number of vertices. | bartleby

Mathematical Excursions (MindTap C...

4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.3, Problem 28ES

Textbook Problem

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If a planar drawing of a graph has twice as many edges as vertices, find a relationship between the number of faces and the number of vertices.

To determine

The relationship between the number of faces and number of vertices.

Explanation of Solution

Given information:

A planar graph has twice as many edges as vertices.

Formula used:

Euler's Formula: v + f = c + 2, where f is the number of faces, v is the number of vertex and c is the number of edges.

Calculation:

Let x be the number of vertices in the planar graph.

⇒v=x

The planar graph has twice as many edges as vertices.

⇒c=2x (Given)

Substituting these values in

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