Hey ! I have trouble answering these questions ! Could someone help me :/

5. Planar Graphs. Let G = (V, E) be a planar graph.

1. (a) A graph is k-regular if every vertex degree is exactly k. How many planar graphs are there which are k-regular for some k, and whose dual is also k-regular for some k, with k not necessarily equal to k?
2. (b)ProvethattheedgesofGcanbepartitionedintoatmostfivedisjointedgessetssuchthateachedgesetformsaforestonV.

6. Dual Graphs. Prove that a planar graph is the dual of its dual if and only if it is connected.

Thank you !