MA-351 Homework 2

Due at 16h59 in my mailbox in HA245, Friday September 14, 2001


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 (b) only.
  2. Consider a 3-D cube as a digraph by letting the arcs point from right-to-left, bottom-to-top, front-to-back. Add to this the additional arc pointing from the right-top-back corner to the left-bottom-front corner. The number of a vertex is the value as a 3-bit 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 by ordering the vertices by ascending numerical value.
    2. the reachability matrix R
    3. write down M3; justify your answer.
  3. DMM, §2.4, Problem 12 on page 59.