Excursions in Modern Mathematics (9th Edition)
Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
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Textbook Question
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Chapter 8, Problem 1E

For the digraph shown in Fig. 8-25, find

a. the indegree and outdegree of A.

b. the indegree and outdegree of B.

c. the indegree and outdegree of D.

d. the sum of the indegrees of all the vertices.

e. the sum of the outdegrees of all the vertices.

Chapter 8, Problem 1E, For the digraph shown in Fig. 8-25, find a.the indegree and outdegree of A. b.the indegree and

Figure 8-25

Expert Solution
Check Mark
To determine

(a)

To find:

The in degree and out degree of A in the given digraph.

Answer to Problem 1E

Solution:

The in degree of A is 3 and out degree of A is 2.

Explanation of Solution

Given:

The given digraph is shown in figure (1).

Excursions in Modern Mathematics (9th Edition), Chapter 8, Problem 1E , additional homework tip  1

Figure (1)

Definitions:

Arc:

An arc XY(XY) indicates that the relationship goes from X to Y.

Indegree:

For a vertex Y, the number of arcs having Y as their ending vertex is called indegree.

Outdegree:

For a vertex X, the number of arcs having X as their starting vertex is called outdegree.

Calculation:

From figure (1) it can be noticed that there are 3 arcs having their ending vertex as A and 2 arcs having their starting vertex as A.

So, the indegree of A is 3 and outdegree of A is 2.

Conclusion:

Thus, the indegree of A is 3 and outdegree of A is 2.

Expert Solution
Check Mark
To determine

(b)

To find:

The in degree and out degree of B in the given digraph.

Answer to Problem 1E

Solution:

The in degree of B is 2 and out degree of B is 2.

Explanation of Solution

Given:

The given digraph is shown in figure (2).

Excursions in Modern Mathematics (9th Edition), Chapter 8, Problem 1E , additional homework tip  2

Figure (2)

Definitions:

Arc:

An arc XY(XY) indicates that the relationship goes from X to Y.

Indegree:

For a vertex Y, the number of arcs having Y as their ending vertex is called indegree.

Outdegree:

For a vertex X, the number of arcs having X as their starting vertex is called outdegree.

Calculation:

From figure (2) it can be noticed that there are 2 arcs having their ending vertex as B and 2 arcs having their starting vertex as B.

So, the indegree of B is 2 and outdegree of A is 2.

Conclusion:

Thus, the indegree of B is 2 and outdegree of B is 2.

Expert Solution
Check Mark
To determine

(c)

To find:

The in degree and out degree of D in the given digraph.

Answer to Problem 1E

Solution:

The in degree of D is 3 and out degree of D is 0.

Explanation of Solution

Given:

The given digraph is shown in figure (3).

Excursions in Modern Mathematics (9th Edition), Chapter 8, Problem 1E , additional homework tip  3

Figure (3)

Definitions:

Arc:

An arc XY(XY) indicates that the relationship goes from X to Y.

Indegree:

For a vertex Y, the number of arcs having Y as their ending vertex is called indegree.

Outdegree:

For a vertex X, the number of arcs having X as their starting vertex is called outdegree.

Calculation:

From figure (3) it can be noticed that there are 3 arcs having their ending vertex as D and no arc having their starting vertex as D.

So, the indegree of D is 3 and outdegree of D is 0.

Conclusion:

Thus, the indegree of D is 3 and outdegree of D is 0.

Expert Solution
Check Mark
To determine

(d)

To find:

The sum of the in degrees of all the vertices.

Answer to Problem 1E

Solution:

The sum of all the indegrees is 10.

Explanation of Solution

Given:

The given digraph is shown in figure (4).

Excursions in Modern Mathematics (9th Edition), Chapter 8, Problem 1E , additional homework tip  4

Figure (4)

Definitions:

Arc:

An arc XY(XY) indicates that the relationship goes from X to Y.

Indegree:

For a vertex Y, the number of arcs having Y as their ending vertex is called indegree.

Outdegree:

For a vertex X, the number of arcs having X as their starting vertex is called outdegree.

Calculation:

From figure (4) it can be noticed that there total 10 arcs, so there will be total 10 indegrees for all the vertices.

Conclusion:

Thus, the sum of all the indegrees is 10.

Expert Solution
Check Mark
To determine

(e)

To find:

The sum of the out degrees of all the vertices.

Answer to Problem 1E

Solution:

The sum of all the outdegrees is 10.

Explanation of Solution

Given:

The given digraph is shown in figure (5).

Excursions in Modern Mathematics (9th Edition), Chapter 8, Problem 1E , additional homework tip  5

Figure (5)

Definitions:

Arc:

An arc XY(XY) indicates that the relationship goes from X to Y.

Indegree:

For a vertex Y, the number of arcs having Y as their ending vertex is called indegree.

Outdegree:

For a vertex X, the number of arcs having X as their starting vertex is called outdegree.

Calculation:

From figure (5) it can be noticed that there total 10 arcs, so there will be total 10 outdegrees for all the vertices.

Conclusion:

Thus, the sum of all the outdegrees is 10.

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Chapter 8 Solutions

Excursions in Modern Mathematics (9th Edition)

Ch. 8 - Prob. 11ECh. 8 - Consider the digraph with vertex-set V={V,W,X,Y,Z}...Ch. 8 - Prob. 13ECh. 8 - Prob. 14ECh. 8 - Prob. 15ECh. 8 - A mathematics textbook consists of 10 chapters....Ch. 8 - Prob. 17ECh. 8 - The digraph in Fig. 8-29 is an example of a...Ch. 8 - Prob. 19ECh. 8 - Wobble, a start-up company, is developing a search...Ch. 8 - A project consists of eight tasks labeled A...Ch. 8 - A project consists of eight tasks labeled A...Ch. 8 - Prob. 23ECh. 8 - Prob. 24ECh. 8 - Prob. 25ECh. 8 - A ballroom is to be set up for a large wedding...Ch. 8 - Prob. 27ECh. 8 - Prob. 28ECh. 8 - Exercises 29 through 32 refer to a project...Ch. 8 - Exercises 29 through 32 refer to a project...Ch. 8 - Prob. 31ECh. 8 - Exercises 29 through 32 refer to a project...Ch. 8 - Prob. 33ECh. 8 - Exercises33 and 34 refer to the Martian Habitat...Ch. 8 - Prob. 35ECh. 8 - Prob. 36ECh. 8 - Prob. 37ECh. 8 - Using the priority list G,F,E,D,C,B,A, schedule...Ch. 8 - Prob. 39ECh. 8 - Using the priority list G,F,E,D,C,B,A, schedule...Ch. 8 - Prob. 41ECh. 8 - Prob. 42ECh. 8 - Prob. 43ECh. 8 - Use the decreasing-time algorithm to schedule the...Ch. 8 - Prob. 45ECh. 8 - Use the decreasing-time algorithm to schedule the...Ch. 8 - Prob. 47ECh. 8 - Consider the project described by the digraph...Ch. 8 - Consider the project described by the digraph...Ch. 8 - Consider the project described by the digraph...Ch. 8 - Consider the project digraph shown in Fig.8-40....Ch. 8 - Consider the project digraph shown in Fig.8-40....Ch. 8 - Prob. 53ECh. 8 - Consider the project digraph shown in Fig.8-41....Ch. 8 - Schedule the Apartments Unlimited project given in...Ch. 8 - Schedule the project given in Exercise26 Table8-5...Ch. 8 - Consider the project described by the project...Ch. 8 - Consider the project digraph shown in Fig.8-43,...Ch. 8 - Prob. 59ECh. 8 - Symmetric and totally asymmetric digraphs. A...Ch. 8 - Prob. 61ECh. 8 - Let W represent the sum of the processing times of...Ch. 8 - You have N=2 processors to process M independent...Ch. 8 - You have N=3 processors to process M independent...Ch. 8 - You have N=2 processor to process M+1 independent...
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