MA-351 Homework 2

Due in my mailbox in HA245 at 9:50am, on Wednesday, September 15, 2004

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 graph (a) only.
2. Consider a 3-D cube as a digraph by letting the arcs point from left-to-right, top-to-bottom, back-to-front, To this, add an arc from the left-front-bottom vertex to the right-back-top vertex. The number of a vertex is the value as a binary number of (left=0/right=1,0=bottom/top=1,0=front/back=1) with the right-bottom-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, again ordering the vertices by ascending numerical value.
   3. write down M³; justify your answer (e.g., "computed in Maple").
3. DMM, §2.4, Problem 12 on page 59.