Homework 1
Math 448 - Fall 2004
Due September 23, 2004 at 11:00 AM
#1. Let G be the graph in gure 2.12 of the textbook. Write down the vertex set V (G)
and the edge family E(G) for this graph.
#2. Draw
i) a simple graph
ii) a non-simple graph with no loop
Homework 9
Math 448 - Fall 2004
Due December 9, 2004 at 12:00 PM
1. Do problem 19.1 on page 92 of the textbook.
2. In April 1975 Martin Gardner, the author of the Mathematical Recreations column in the
magazine Scientic American published the map below as
Homework 5
Math 448 - Fall 2004
Due October 28, 2004 at 12:00 PM
#1. Do problem 9.3 on page 46 of the textbook.
#2. Do problem 9.5 on page 46 of the textbook.
#3. Prove that any tree with more than 1 vertex is not an Eulerian graph.
Hint: Look at the comm
Homework 3
Math 448 - Fall 2004
Due October 7, 2004 at 12:00 PM
#1. Do part i) of problem 9 on page 20 of the textbook.
#2. Find a solution of the four cubes problem for the set of cubes below.
#3. Do problem 4 on page 25 of the textbook.
#4. Do part i) o
Homework 2
Math 448 - Fall 2004
Due September 30, 2004 at 12:00 PM
#1-3. Do problems 2.11, 2.13 and 2.14 on page 16 of the textbook. On problem 2.14,
explain why your answers are correct.
#4. Let G be the graph in gure 2.24 of the book. Let v be vertex 5
Homework 4
Math 448 - Fall 2004
Due October 21, 2004 at 12:00 PM
#1. Prove Corollary 6.4 on page 33 of the textbook.
Hint: To show that there is a semi-Eulerian trail, start by adding a new edge connecting
the two vertices of odd degree.
#2. Do parts i),
Homework 7
Math 448 - Fall 2004
Due November 18, 2004 at 12:00 PM
1. Do problems 2, 3, 6 and 8 on pages 64-65 of the textbook.
Note: There is a solution to problem 3 in the back of the book. In order to get credit for
this problem, you need to explain how
Homework 10
Math 448 - Fall 2004
1. Do problem 21.1 on page 99 of the textbook.
2. Do problem 21.2 on page 99 of the textbook.
3. Find the chromatic polynomials for each of graphs 15, 25 and 29 in gure 2.9 on page 11
of the textbook.
4. Prove that if G is
Homework 6
Math 448 - Fall 2004
Due November 4, 2004 at 12:00 PM
#1. Do problem 10.3 on page 51 of the textbook.
Note: It might help for you to recall that
e = lim
n
1
1+
n
n
.
#2. Find the number of spanning trees in the graph below.
#3. In the second pr
Homework 8
Math 448 - Fall 2004
Due December 2, 2004 at 12:00 PM
1. Find the duals of the graph in gure 8.8 on page 42 of the textbook (ignore the weights)
and the graph in gure 7.7 on page 37 of the textbook.
2. Do problem 15.3 on page 76 of the textbook