‫المملكة العربية السعودية‬
‫وزارة التعليم العالي‬
‫جامعة االميرة نورة بنت عبد الرحمن‬
‫كلية علوم الحاسب والمعلومات‬
Kingdom of Saudi Arabia
Ministry of Higher Education
Princess Noura bint Abdulrahman University
College of Computer & Information Sciences
HW-9
Name:
ID:
Section:
QUESTION #1 :
Determine whether the graphs shown below have directed or undirected
edges, whether they have multiple edges, and whether they have one or
more loops.
Un Direct edges
B
b
Direct
edges
multiple edges
multiple edges
A
No loops.
more loops
QUESTION #2 :
For following graph, determine:
-The number of vertices and edges.

4 vertices and 8 edges
-The in-degree and out-degree of each
vertex for the given directed multi-graph.
In-degrees: deg -(a) = 2, deg -(b) = 3, deg (c) = 2 deg -(d) = 1.
Out-degrees: deg+(a) = 2, deg+(b) = 4,
deg+(c) = 1, deg+(d) = 1,
-
‫المملكة العربية السعودية‬
‫وزارة التعليم العالي‬
‫جامعة االميرة نورة بنت عبد الرحمن‬
‫كلية علوم الحاسب والمعلومات‬
Kingdom of Saudi Arabia
Ministry of Higher Education
Princess Noura bint Abdulrahman University
College of Computer & Information Sciences
The sum of the in-degrees of the vertices and the sum of the outdegrees of the vertices directly. Show that they are both equal to
the number of edges in the graph.
 deg v    deg v  E

vV

vV
Sum of In-degrees=2+3+2+1= 8
Sum of Out-degrees= 2+4+1+1= 8
Sum of In-degrees= Sum of Out-degrees=8
QUESTION #3 :
Determine whether the graphs shown below are bipartite. Justify your
answer.
1
1. Yes because :
Its vertex set can be partitioned into the two sets
V1= { b, e, d} and V2= {a, c}
2. Yes because :
Its vertex set can be partitioned into the two sets
V1= {a, b, e, d} and V2= {f, c}
2
b
‫المملكة العربية السعودية‬
‫وزارة التعليم العالي‬
‫جامعة االميرة نورة بنت عبد الرحمن‬
‫كلية علوم الحاسب والمعلومات‬
Kingdom of Saudi Arabia
Ministry of Higher Education
Princess Noura bint Abdulrahman University
College of Computer & Information Sciences
QUESTION #4 :
Construct a precedence graph for the following program:
S1 a := 2
S2 b := 1
S6
S3 c := b+1
S4 d := b+ 3
S4
S5 e := a + d
S5
S6 f:= d +c + a
S3
S1
S2
QUESTION #5:
Given the following graph:
a. Represent the graph with adjacency list.
b. Represent the graph with adjacency matrices.
Vertex
A
B
C
D
adjacency list
b,d,c
a,d
a,d
a,b,c
‫المملكة العربية السعودية‬
‫وزارة التعليم العالي‬
‫جامعة االميرة نورة بنت عبد الرحمن‬
‫كلية علوم الحاسب والمعلومات‬
Kingdom of Saudi Arabia
Ministry of Higher Education
Princess Noura bint Abdulrahman University
College of Computer & Information Sciences
Adjacent matrices:
a
b
c
d
a
0
1
1
1
b
1
0
0
1
c
1
0
0
1
d
1
1
1
0
QESTION #6:
Draw a graph with the given adjacency matrix.
𝟎 𝟏 𝟎
[𝟏 𝟎 𝟏]
𝟎 𝟏 𝟎
Graph draw:
QESTION #7:
Does each of these lists of vertices form a path in the following graph?
Which are simple? Which are circuits? What are the lengths of those that
are paths?
i. a,e,b,c,b.
ii. e,b,a,d,b,e.
iii. c,b,d,a,e,c.
‫المملكة العربية السعودية‬
‫وزارة التعليم العالي‬
‫جامعة االميرة نورة بنت عبد الرحمن‬
‫كلية علوم الحاسب والمعلومات‬
Kingdom of Saudi Arabia
Ministry of Higher Education
Princess Noura bint Abdulrahman University
College of Computer & Information Sciences
I.
a,e,b,c,b.
Is it simple?
–
No, because it hase the same edge more than one.
What is the length? –
3 –
Does it have any circuits?
no –
II.
III.
–
e,b,a,d,b,e.
this list of vertices e,b,a,d,b,e. does not form a path in the
following graph.
IV. c,b,d,a,e,c.
Is it simple? –
yes
What is the length? –
5 –
Does it have any circuits?
yes –
–
‫المملكة العربية السعودية‬
‫وزارة التعليم العالي‬
‫جامعة االميرة نورة بنت عبد الرحمن‬
‫كلية علوم الحاسب والمعلومات‬
Kingdom of Saudi Arabia
Ministry of Higher Education
Princess Noura bint Abdulrahman University
College of Computer & Information Sciences
QESTION #8:
Determine whether the given graph is connected.
1
yes; it is connected
QESTION #9:
2
No , it is connected
Determine whether each of these graphs is strongly connected and if not,
whether it is weakly connected.
1
2
1, This graph is not strongly connected. Why not? Because there is no
.directed path between d and c,c and b,
However, it is weakly connected. (Imagine this graph as an undirected
).graph
2, This graph is not strongly connected. Why not? Because there is no
.directed path between a and b,b and c,
However, it is weakly connected. (Imagine this graph as an undirected
graph.)