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.
- DMM, §2.3, Problem 1 on page 49 for graph (a) only.
- 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
- the adjacency matrix M by ordering the vertices
by ascending numerical value.
- the reachability matrix R, again ordering the vertices
by ascending numerical value.
- write down M3; justify your answer (e.g.,
"computed in Maple").
- DMM, §2.4, Problem 12 on page 59.