Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 10 - Geometry - 10.7 Beyond Euclidean Geometry - Exercise Set 10.7 - Page 677: 27

Answer

In the geometry of graphs, if you can trace a graph without lifting the pencil from the paper and without tracing an edge more than once, that is, continuously and without repeating, then the graph is called traversable.

Work Step by Step

According to the graph theory proposed by Swiss mathematician Euler, a graph can only be traversed if we can continuously trace it and do not overlap any edge, that is, each edge is traced only once. He also proved the following rules of traversability: 1. If all the vertices of the graph are even, it can be traversed. For traversing such a graph, one should start with any vertex and end at the point of beginning. 2. If there are two odd vertices in a graph, it can be traversed. One should start tracing at any of the odd vertices and finish at the other odd vertex of the graph. 3. A graph that has more than two odd vertices is not traversable.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.