1.
(a)
Draw a connected planar graph with 5 vertices and 5 edges. How many faces (including the βoutsideβ face) does your graph have?
Number of faces:
(b)
Now add a single edge to your graph, between two vertices that are not already adjacent. Assuming the resulting graph is still planar, list the number of vertices, edges, and faces it now has.
Vertices: ; Edges: ; Faces:
(c)
Now add another edge to the graph, this time to a new vertex. Assuming the resulting graph is still planar, list the number of vertices, edges, and faces it now has.
Vertices: ; Edges: ; Faces: