Graph Theory Practice: SET G: (Plane graphs)
Department of Mathematics and Computer Studies
York College (CUNY)
Jamaica, New York
1. For the graph G below:
a. Draw G - v for each vertex of G
b. Draw G - e for each edge of G
c. List the cut vertices of G if any.
d. List the bridges (cut edges) of G if any.
e. Draw the line graph of G. If the line graph of G is planar draw a plane embedding of the line graph.
2. Repeat the questions above for the graph G below:
f. Draw the medial graph of the graph above. How many vertices, edges and faces does this medial graph have?
g. Is the graph above 3-polytopal? If not, what is the minimum number edges that can be added to the graph to make it 3-polytopal?
h. Does the graph above have an Eulerian circuit? If so write one down. If not, give a reason, and find a Chinese Postman tour for this graph.