Do for discussion Thurs. 2/5 (additional problem):

# BB1.

Go to announcements | course information | homework list | previous homework | next homework.

BB1. This concerns Theorem 1.1.2 and the example G_{0}. I'll follow the book's notation.
The sequence

(S1) (4, 4, 4, 3, 3, 3, 2, 2, 1)

is known to be graphic, because it is the degree sequence of G_{0}. From (S1) the rule of Theorem 1.1.2 gives

(S2) (3,3,2,2,3,2,2,1),

which, rearranged in descending order, is

(S3) (3,3,3,2,2,2,2,1).

- (a) In this example what are s, t
_{1}, ..., t_{s}, n, d_{1}, ..., d_{n}? (Give their values.) - (b) Label the vertices of G
_{0}by S, T_{1}, ..., T_{s}, D_{1}, ..., D_{n}as in the proof of the theorem.)**Do this problem for each of the three possible choices of S.** - (c) If you delete vertex S, does the new graph G
_{0}- S have (S3) as its degree sequence? - (d) Use
*the method in the proof*to modify G_{0}so that, when you delete S, you do get (S3) as the degree sequence of the new graph.