1. Is there a BART ride (see Exercise 29) if we disregard the difference between different rapid transit lines (that is, if adjacent stations have only one edge connecting them)? If your answer is...

1. Is there a BART ride (see Exercise 29) if we disregard the difference between different rapid transit lines (that is, if adjacent stations have only one edge connecting them)? If your answer is “yes,” describe the drive. If your answer is “no,” explain why.

2.
In this exercise, you will find the relationship between the number of edges in a graph and the sum of the degrees of all of the vertices.

 a. Complete the chart in Figure 9.38.

b. Using the result of part (a), make a guess as to the relationship between the number of edges in a graph and the sum of the degrees of all of the vertices.

 c. How many vertices must an edge connect?

d. How much does an edge contribute to the degree of each of the vertices it connects?

e. Use the results of parts (c) and (d) to explain why your guess in part (a) must be correct.