110
101
M
R
=
M
S
=
010
(a)
If we assume that the matrices were constructed using the
order listed above for the set A, then
R=
(b)
What is the matrix representing R
∩
S?
M
R
∩
S
=
(c)
Construct the digraph representing S in the space below.
4. (10 pts.)
(a) Using the prefix code a:001, b:0001, e:1,
r:0000, s:0100, t:011, and x:01010, decode the following bit
string:
0111001000100100000100
(b)
Construct the ordered rooted binary tree representing the
following expression:
(C  (A
∪
B
)
)=(
(
CA
)
∩
(C  B))
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5. (15 pts.)
(a) Draw a directed graph G
1
whose adjacency
matrix is
0110
1001
.
(b)
Now draw an undirected graph G
2
which is represented by the
adjacency matrix in part (a) of this problem.
(c)
Is G
2
=(
V
2
,E
2
), above, isomorphic to the simple graph
G
3
V
3
,E
3
) given below?
Either display an isomorphism f:V
2
> V
3
or very briefly explain why there is no such function by
revealing an invariant that one graph has that the other doesn’t.
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 Spring '08
 STAFF
 Graph Theory, pts, Binary relation, Tree traversal, Nested set model

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