MA-351 Homework 2

Due at 4:59pm in my mailbox in HA 245, Monday September 24, 2007


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.
Note my office hours on my schedule.

  1. DMM, §2.3, Problem 1 on page 49 for digraph (a) 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. The number of a vertex is the value as a binary number of (0=left/right=1, 1=bottom/top=0, 1=front/back=0)2 with the right-top-back vertex having the number (100)2 = 4. There is an additional arc from vertex 0 (left-top-back) to vertex 3 = (011)2 (left-bottom-front). 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 (e.g., "computed in Maple").
  3. DMM, §2.4, Problems 12 on page 59.