Honors Discrete 8.2 DIGRAPH Worksheet Name: __ANSWER KEY_____
1) Draw each of the following digraphs:
a. Arc-Set
={AB, AC, AE, BE, CD, CB, DE, EA, EB}
A
b. Arc- Set
= {PQ, PR, PS, QS, QT, QP, RS, RT, ST, TS, TP}
B
P
Q
E
C
R
T
D
c. Vertex-Set = {W, X, Y, Z} and with incidence …
W incident from X and Y;
X incident to W and Z;
Y incident from Z, X, and W;
Z incident to W and X
2) For each of the following digraphs:
DIGRAPH #1
W
X
Z
Y
c. Find a path from C to E.
i. Length of 2 arcs: C, D, E
B
ii. Length of more than 2 arcs
Length 3: C, A, D, E
Length 4: C, A, B, D, E
D
E
A
S
d. Find a cycle starting at vertex A.
A, B, D, E, C, A
A, D, E, C, A
A, D, E, B, D, E, C, A
C
a. Find the indegree of each vertex.
A = 1, B = 2, C = 1, D = 4, E = 2
e. Finish all of the incidence relations:
i. A is incident to … B, D
ii. D is incident from … B, A, C, E
iii. E is incident from … D, D
iv. B is incident to … D
b. Find the outdegree of each vertex.
A = 2, B = 1, C = 2, D = 2, E = 3
DIGRAPH #2
B
A
C
D
J
E
I
F
H
a. Find the indegree of each vertex.
A=2
B=0
C=1
E=1
F=2
G=1
I=1
J=2
G
D=3
H=1
b. Find the outdegree of each vertex.
A=1
B=2
C=2
E=1
F=0
G=0
I=2
J=1
c. Find a path from C to E.
i.
Length of 2 arcs: C, D, E
ii. Length of more than 2 arcs
C, A, H, D, E
C, A, H, I, D, E
C, A, H, I, J, C, D, E
d. Find a cycle starting at vertex A.
A, H, I, J, C, A
D=2
H=3
E is incident from … D
B is incident to … A, J
iii.
iv.
e. Finish all of the incidence relations:
i.
A is incident to … H
ii.
D is incident from … C, I, H
3) For the digraph with arc-set {AB, AC, BC, CD, CE, DA, DB, EA, EC, EB}
a. Find the INDEGREE of each vertex.
A=2
B=3
C=3
D=1
E=1
b. Find the OUTDEGREE of each vertex.
A=2
B=1
C=2
D=2
E=3
4) Draw the project digraph for each situation: Use separate sheet as needed
HINT: Identify your START tasks
a. A project of four tasks: Task A (3 hours), Task Q (2 hours), Task X (4 hours), and Task F (2 hours)
such that task X must precede tasks A and F, and task Q must precede tasks X and A.
Q
START(
0)
A
b. Use the table to create a project digraph.
Task
Time Precedence Relations
X
X
X→ W, Z→ W
Y→X
W
X
5
7
Y
10
Z
8
Y→Z
Task
Time
Precedence Relations
L
17
M → L, N→ L
M
12
O → M, P→ M
N
11
O→ N
O
8
P
14
Q
21
F
W
START(0)
P → Q, L → Q
END(0
)
END(0)
Y
Z
N
O
L
M
START(0
)
Q
END(0
)
P
Task
A
B
C
D
E
F
G
H
I
Precedence
Relations
A→B
B→C, D→C
A→D, G→D
G→E, D→E
C→F, E→F
F→H, E→H
F→I, B→I
B
I
C
A
END
F
D
START
G
E
H