Combinatorial and Discrete Geometry: Sheet X

Transformations of Plane Graphs

Prepared by:

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

web page:

1. For each of the graphs below:

a. Write down its degree sequence and its face vector

b. Draw the dual graph

c. Draw the medial graph

d. Draw the line graph

e. Draw the graph where an edge is replaced by a hexagon

(If the graph you get above after the transformation is plane, find the face coloring number of the transformed graph.)

Perhaps it will surprise you that the two graphs below are isomorphic. Work with the plane graph on the right and verify that the two graphs are isomorphic. This graph arises as the graph of the regular icosahedron.