# Dual Graph Every planar graph has what is called a dual graph. To form the dual graph, start with a planar drawing of the graph. With a different-color pen, draw a dot in each face (including the infinite face). These will be the vertices of the dual graph. Now, for every edge in the original graph, draw a new edge that crosses over it and connects the two new vertices in the faces on each side of the original edge. The resulting dual graph is always itself a planar graph. (Note that it may contain multiple edges.) The procedure is illustrated below. Draw the dual graph of each of the planar graphs below. For each of the graphs in part a, count the number of faces, edges, and vertices in the original graph and compare your results with the numbers in the dual graph. What do you notice? Explain why this will always be true. Start with your dual graph of the first graph in part a, and find its dual. What do you notice?

### Mathematical Excursions (MindTap C...

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

### Mathematical Excursions (MindTap C...

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

#### Solutions

Chapter 5.3, Problem 30ES
Textbook Problem

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