Homework 3

This homework is due on Thursday, February 25, right before class.

  1. Draw the plane graph of the following polyhedron:

  2. A connected plane graph has nine vertices having degress 2, 2, 2, 3, 3, 3, 4, 4, and 5. How many edges are there? How many regions?
  3. Is there a plane graph without vertices of degree 6 or less? Try to find one, and if you don't succeed, describe why you cannot find some. A proof would even be better.
  4. Find the dual of the following graph.