Polyhedra and Graphs

Prepared by:

Joseph Malkevitch
Department of Mathematics and Computer Studies
York College (CUNY)
Jamaica, New York 11451

Email: malkevitch@york.cuny.edu (for additions, suggestions, and corrections)

1. For each of the graphs below:

a. Is the graph the vertex-edge graph of some convex polyhedron? Is the graph the vertex-edge graph of some non-convex polyhedron?

b. How many vertices does the graph have? How many edges? How many faces?

c. What are the valences of the vertices? What are the number of sides that the faces of the polyhedron (assuming that it is the graph of a polyhedron) have?

d. If the graph has crossing at point that are not vertices as it is drawn, redraw the graph in the plane so that such crossings are avoided.