Problems 1-4

There questions are basically definitions and procedures. Read the book and then paraphrase each in your own words.
Problems 5-12

Review the definition of a tree and see Examples 1 and 2.
Problems 13-20

Review the definition of a spanning tree and remove edges as shown in Example 4.
Problems 21-26

It is generally difficult to find all of the spanning trees, but these trees are simple enough that you can proceed systematically to find them all.
Problems 27-32

Read the directions carefully to understand the transition from ball-and-stick model to bond-line drawing to tree diagram, as shown in Figure 9.33.
Problems 33-42

Use Kruskal’s algorithm to find the minimum spanning tree, as shown in Example 6.
Problems 43-44

Use the number-of-vertices-and-edges-in-a-tree theorem to answer these questions.
Problems 45-47

Draw a tree and then use the number-of-vertices-and-edges-in-a-tree theorem to answer these questions.
Problems 48-49

Use the number-of-vertices-and-edges-in-a-tree theorem.
Problems 50-54

Use Krukal’s algorithm as shown in Examples 6 and 7.
**Note:** Homework Hints are given only for the Level 1 and Level 2 problems.

However, as you go through the book be sure you look at all the examples in the text. If you need hints for the Level 3 problems, check some sources for help on the internet (see the LINKS for that particular section. As a last resort, you can call the author at (707) 829-0606.

On the other hand, the problems designated “Problem Solving” generally require techniques that do not have textbook examples.

There are many sources for homework help on the internet.

**Algebra.help**

Here is a site where technology meets mathematics. You can search a particular topic or choose lessons, calculators, worksheets for extra practice or other resources.

**http://www.algebrahelp.com/**

**Ask Dr. Math**

Dr. Math is a registered trademark. This is an excellent site at which you can search to see if your question has been previously asked, or you can send your question directly to Dr. Math to receive an answer.

**http://mathforum.org/dr.math/**

**Quick Math**

This site provides online graphing calculators. This is especially useful if you do not have your own calculator.

**http://www.quickmath.com/**

**The Math Forum** @ Drexel

This site provides an internet mathematics library that can help if you need extra help. For additional homework help at this site, click one of the links in the right-hand column.

**http://mathforum.org/**

There questions are basically definitions and procedures. Read the book and then paraphrase each in your own words.

Review the definition of a tree and see Examples 1 and 2.

Review the definition of a spanning tree and remove edges as shown in Example 4.

It is generally difficult to find all of the spanning trees, but these trees are simple enough that you can proceed systematically to find them all.

Read the directions carefully to understand the transition from ball-and-stick model to bond-line drawing to tree diagram, as shown in Figure 9.33.

Use Kruskal’s algorithm to find the minimum spanning tree, as shown in Example 6.

Use the number-of-vertices-and-edges-in-a-tree theorem to answer these questions.

Draw a tree and then use the number-of-vertices-and-edges-in-a-tree theorem to answer these questions.

Use the number-of-vertices-and-edges-in-a-tree theorem.

Use Krukal’s algorithm as shown in Examples 6 and 7.