**Plane Graphs**

prepared by:

Joseph Malkevitch

Mathematics Department

York College (CUNY)

Jamaica, New York 11451

email: malkevitch@york.cuny.edu

1. For each of the graphs below which is plane, find:

a. The number of vertices b. The number of edges

c. The number of faces

e. The number of vertices with each valence (degree) i.

f. The number of faces with i sides.

g. Verify that and each gives twice the number of edges in the graph.

h. Draw the medial graph of each graph shown.

i. For each graph graph determine if it has an Eulerian circuit, an (open) Eulerian trail, a Hamiltonian circuit, or a Hamiltonian path?

G

H

I

J