## Regular planar graphs

Prove or disprove : For each \(n\in \mathbb{N}\), there is a simple connected \(4\)-regular planar graph with more than \(n\) vertices.

Prove that a planar, simple, connected, \(6\)-regular graph does not exist.

Prove or disprove : For each \(n\in \mathbb{N}\), there is a simple connected \(4\)-regular planar graph with more than \(n\) vertices.

Prove that a planar, simple, connected, \(6\)-regular graph does not exist.