Then the two edge path is:
Step 1: From
a
1
a
2
…
a
k
…
a
n
goto
´
a
1
´
a
2
´
…b
k
´
a
k
+
1
…
´
a
n
=
´
b
1
´
b
2
´
…b
k
´
b
k
+
1
…
´
b
n
.
Step 2: From
´
b
1
´
b
2
´
…b
k
´
b
k
+
1
…
´
b
n
to
b
1
b
2
…
b
k
b
k
+1
b
k
+2
…
b
n
.
6

6(a)
(10 points)
Conduct a DFS for the following graph. Please label each vertex
u
with the discovery
time and the finish time
d
(
u
)/
f
(
u
). You should start the traversal from vertex
a
, and
follow the alphabetic order whenever you need to make a decision among multiple
choices.
Solution:
(b) (5 points)
List all edges that belong to each of the following sets:
The set of back edges:
(
e
,
b
), (
g
,
a
), (
h
,
f
),
The set of forward edges:
(
a
,
e
), (
a
,
f
), (
e
,
j
), (
d
,
j
)
The set of cross edges:
(
g
,
h
)
7

(c)
(5 points)
Identify the strongly connected components and draw the component graph.
8

7 (15 points)
Use Dijkstra’s algorithm to find the shortest path tree for the following graph. Please take
the vertex
s
as the source. You must show detailed steps, one figure for each step.
(Initialization is given in the following graph.)
Solution:
Step 1
Step 2
9

Step 3
Step 4
10

Step 5
Step 6
Step 7
11

Step 8
The shortest path tree is:
12

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- Fall '18
- Eric Swartz