MA-351 Homework 2

Due at 9:50 in class, Thursday September 9, 1999

Calculations necessary for these problems may be done either by hand or with Maple. Solutions may be submitted in person in class, or you may email an ASCII text, Maple Worksheet (.mws), html, or postscipt/pdf-formatted document to me (kaltofen@math.ncsu.edu).
Note my office hours on my schedule.

1. DMM, §2.3, Problem 1 on page 49 for graph (a) only.
2. Consider a 3-D cube as a digraph by letting the arcs point from left-to-right, bottom-to-top, front-to-back. The number of a vertex is the value as a binary number of (left=0/right=1,bot/top,front/back) with the right-bot-front vertex having the number 4. Please give
   1. the adjacency matrix M
   2. the reachability matrix R
   3. write down M³; justify your answer.
3. DMM, §2.4, Problem 11 on page 59.