Math 5, Winter 2000

3

Midterm Problem-Solving Exam

(8 points)

8.

The complete bipartite graphwith parts of size mand nis constructed as
follows: Draw mvertices on the left and nvertices on the right; then
connect all the vertices on the left to all the vertices on the right with
edges. Below is shown the complete bipartite graph with parts of size 3
and 4.

(a)

For what values of mand nis the complete bipartite graph with
parts of size mand nEulerian? Explain.
For what values of mand nis the complete bipartite graph with
parts of size mand nHamiltonian? Explain.

(b)

(6 points)

9.

Start with the Maple worksheet ISBN.mws (on the Math 5 website). For
each part of this problem, you should use the worksheet to answer the
question, and then submit a printed copy of the worksheet showing your
solution.

(a)

Verify that 1-85894072-9 is a valid ISBN. [Note: this book is
published in England.]
Find a book of your own that is published in the United States.
Verify the validity of its ISBN.
Suppose your book were published in England instead of in the
U.S. What would be the check digit?

(b)

(c)