Planar Graph Problems

From Exercises 10 and 12 of Section 7.3 in Introduction to Discrete Mathematics by D. Ensley and W. Crawley, to be published by John Wiley and Sons, 2005.

For each of the following graphs, determine if it is planar or not by dragging the nodes until the edges of the graph do not cross, if possible. Warning: If you do not manage to arrange the edges so that they do not cross, you have not proven that the graph is non-planar. In this case, your answer is simply an informed conjecture. You will need to give a reason why the graph is non-planar.

Copyright 2005 by Douglas E. Ensley. See http://www.ship.edu/~deensl/DiscreteMath/ for more Flash applets for Discrete Mathematics. Please direct questions and comments to deensl@ship.edu.