Summary: Graph Theory Handout Math 105, Fall 2010 Page 1
Definition: A graph is planar if we can draw it on the plane (a flat surface) with no crossing
edges. If the graph is actually drawn in such a way, we say that the drawing is a plane graph.
Example: What about paths, cycles, wheels, trees? What about complete graphs? See
Definition: If G is a connected plane graph, it divides the plane into different regions,
which are called faces. Note: The "outside" of a graph is always one face.
Graph Theory Handout Math 105, Fall 2010 Page 2
1. Try to draw each of the following complete graphs as a plane graph.
Ki Drawn as a plane graph Is Ki planar?