Math 11

Discrete Mathematics

Readings Check section 11.3

Read Section 11.3.

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1) What is the degree of an pendant vertex?

2) What does the notation mean?

3) What is the value of |E| if = 200 ?

4) Can there exist a graph with |V| = 9 vertices, all with degree 3 ? [see corollary 11.1]

5) Suppose that a 4-regular graph has |V| = 20 vertices. What is the value of |E| ?

[See example 11.11 and use Theorem 11.2].

6) How many vertices are in Qn , the nth dimensional hypercube?

7) In Qn under what condition are two vertices joined by an edge?

8) In Q5, what is the distance between the vertices 10010 and 01101 ?

9) How many edges are in Q10 ? [page 533]

10) Why is it impossible to solve the "Seven Bridges of Konigsberg" problem? That is, why is it impossible to find an Euler circuit for the graph in figure 11.37(b)?

11) If G is a directed, connected graph with no isolated vertices and id(v) = od(v) for all vertices v in G, what can we conclude about G? [Theorem 11.4]

After submitting this form, go on to watch the videos, read the notes, and start the homework assignment for section 11.3. 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 1.3.