Math 12

Discrete Mathematics

Readings Check section 12.1

Read Section 12.1

Type in the answers below each question and email the completed document to me, or print out the document and fill it out by hand and email a scan or photo of it to me.

1) Why is G2 in figure 12.1 not a tree? Why is G3 not a tree?

2) If a and b are distinct vertices in a tree, is the path that connects them unique? (Theorem 12.1)

3) Does every graph have a spanning tree? (Theorem 12.2)

4) If a tree has 5000 vertices, how many edges does it have? (Theorem 12.3)

5) What is the minimum number of pendant vertices that a tree must contain? (Theorem 12.4)

6) Examples 12.1 and 12.2 show an interesting application of trees to organic chemistry. If an alkane has 20 carbon atoms, how many hydrogen atoms does it contain?

7) Is it true that every edge in a tree is a bridge? [See also notes for 11.5.]

After submitting this form, go on to watch the videos, read the notes, and start the homework assignment for section 12.1. Ask any questions that arise at any point in the process. When the homework assignment is done, and you feel that you have a solid understanding of the homework and the section, then take the quiz for section 12.1.