prepared by:
Joseph Malkevitch
Mathematics Department
York College (CUNY)
Jamaica, New York 11451
email: malkevitch@york.cuny.edu
1. Derive an Euler relation for 4-valent plane graphs.
2. For the face vectors below, try if possible to construct a plane 3-valent 3-connected graph with the given numbers of faces.
a.
b.
c.
3. Draw diagrams of all the graphs of the 5 Platonic solids.
4. If one erects a combinatorial square pyramid on each face of the plane graph of a cube, write down the vertex and face vectors of the resulting graph.
Hint: (The diagram below indicates what has to be done on each face.)
