More Final Review Problems
Prepared by:
Joseph Malkevitch
Department of Mathematics and Computer Studies
York College (CUNY)
Jamaica, New York
email:
malkevitch@york.cuny.edu
web page:
http://york.cuny.edu/~malk/
1. Given the graph G below:
a. Draw G - e
b. Draw G - f
c. Draw G - edge bd
d. Draw G - a
e. Draw G - edge ie
f. List the bridge edges of G
g. List the cut vertices of G
h. Draw the graph induced by the set of vertices: { a, d, e, i }
i. Draw the graph induced by the set of vertices: {a, b, d, e, i }
j. Does the graph which is a 4-cycle arise as an induced subgraph of G?
k. Find a spanning tree of G
l. Draw the dual of the graph obtained by finding G - f as well as the "isolated" vertices h and g which result.
2. Given the graph H below:
a. Draw the dual of H ; b. If pk denotes the number of faces with k sides in a plane graph, find the pk values for H and its dual; c. Find the minimum number of colors to color i. the vertices ii. the faces of H.