The statement that best describes fault isolation is that Fault Isolation is known to be the area of knowing the cause of an issue.
What is fault isolation?Fault Isolation is also known to be the way or method use in knowing the cause of an issue.
It is also known as fault diagnosis as it helps to deals with a lot of methods that can help one to be able to isolate the component or the device that is causing or leading to the error.
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In Exercises 1–4 construct the dual graph for the map shown.
Then find the number of colors needed to color the map so
that no two adjacent regions have the same color.
Answer:
10.8 Graph Coloring
A coloring of a simple graph is the assignment of a color to each vertex of the graph so that no
two adjacent vertices are assigned the same color.
Chromatic number
The chromatic number of a graph is the least number of colors needed for a coloring of this graph.
The Four Color Theorem
The chromatic number of a planar graph is no greater than four.
10.8 pg. 733 # 3
Construct the dual graph for the map shown. Then find the number of colors needed to color the
map so that no two adjacent regions have the same color.
a
b c d e
f
At least three colors are needed to color the
graph because of triangle 4abc exists in the
graph.
10.8 pg. 733 # 7
Find the chromatic number of the given graph.
a
b
c
d
Since this graph forms two triangles, 4abd and
4bcd, we can color this graph with at least 3
colors where a and c are the same colors.
a
b
c
d
10.8 pg. 733 # 9
Find the chromatic number of the given graph.
1
ICS 241: Discrete Mathematics II (Spring 2015)
a
e
b
c
d
This graph can be colored with two colors like
shown.
a
e
b
c
d
10.8 pg. 734 # 19
The mathematics department has six committees, each meeting once a month. How many different
meeting times must be used to ensure that no member is scheduled to attend two meetings at the
same time if the committees are C1 = {Arlinghaus, Brand, Zaslavsky}, C2 = {Brand, Lee, Rosen},
C3 = {Arlinghaus, Rosen, Zaslavsky}, C4 = {Lee, Rosen, Zaslavsky}, C5 = {Arlinghaus, Brand},
and C6 = {Brand, Rosen, Zaslavsky}?
We will first draw the intersection graph of the given sets.
C1 C2
C3
C5 C4
C6
From here, it is easy to see that we need at least 5 colors like so:
C1 C2
C3
C5 C4
C6
Therefore, 5 meeting times are needed. Committees C4 and C5 can meet at the same time.
Explanation:
done-_-