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. Figure 8-25

Question

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Answer 1

Textbook Question

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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 1

Figure (1)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 2

Figure (2)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 3

Figure (3)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 4

Figure (4)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 5

Figure (5)

Definitions:

Arc:

An arc XY(X→Y) 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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Answer 2

Textbook Question

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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 1

Figure (1)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 2

Figure (2)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 3

Figure (3)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 4

Figure (4)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 5

Figure (5)

Definitions:

Arc:

An arc XY(X→Y) 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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Answer 3

Textbook Question

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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 1

Figure (1)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 2

Figure (2)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 3

Figure (3)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 4

Figure (4)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 5

Figure (5)

Definitions:

Arc:

An arc XY(X→Y) 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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Answer 4

Textbook Question

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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 1

Figure (1)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 2

Figure (2)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 3

Figure (3)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 4

Figure (4)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 5

Figure (5)

Definitions:

Arc:

An arc XY(X→Y) 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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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 1

Figure (1)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 2

Figure (2)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 3

Figure (3)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 4

Figure (4)

Definitions:

Arc:

An arc XY(X→Y) 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

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 5

Figure (5)

Definitions:

Arc:

An arc XY(X→Y) 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.

Answer 8

Expert Solution

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 1

Figure (1)

Definitions:

Arc:

An arc XY(X→Y) 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.

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

(a)

To find:

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

Answer 13

Answer to Problem 1E

Solution:

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

Answer 14

Explanation of Solution

Given:

The given digraph is shown in figure (1).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 1

Figure (1)

Definitions:

Arc:

An arc XY(X→Y) 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.

Answer 15

Expert Solution

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 2

Figure (2)

Definitions:

Arc:

An arc XY(X→Y) 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.

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

(b)

To find:

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

Answer 20

Answer to Problem 1E

Solution:

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

Answer 21

Explanation of Solution

Given:

The given digraph is shown in figure (2).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 2

Figure (2)

Definitions:

Arc:

An arc XY(X→Y) 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.

Answer 22

Expert Solution

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 3

Figure (3)

Definitions:

Arc:

An arc XY(X→Y) 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.

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

(c)

To find:

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

Answer 27

Answer to Problem 1E

Solution:

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

Answer 28

Explanation of Solution

Given:

The given digraph is shown in figure (3).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 3

Figure (3)

Definitions:

Arc:

An arc XY(X→Y) 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.

Answer 29

Expert Solution

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 4

Figure (4)

Definitions:

Arc:

An arc XY(X→Y) 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.

Answer 30

Expert Solution

Answer 31

Expert Solution

Answer 32

Expert Solution

Answer 33

To determine

(d)

To find:

The sum of the in degrees of all the vertices.

Answer 34

Answer to Problem 1E

Solution:

The sum of all the indegrees is 10.

Answer 35

Explanation of Solution

Given:

The given digraph is shown in figure (4).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 4

Figure (4)

Definitions:

Arc:

An arc XY(X→Y) 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.

Answer 36

Expert Solution

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).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 5

Figure (5)

Definitions:

Arc:

An arc XY(X→Y) 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.

Answer 37

Expert Solution

Answer 38

Expert Solution

Answer 39

Expert Solution

Answer 40

To determine

(e)

To find:

The sum of the out degrees of all the vertices.

Answer 41

Answer to Problem 1E

Solution:

The sum of all the outdegrees is 10.

Answer 42

Explanation of Solution

Given:

The given digraph is shown in figure (5).

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC, Chapter 8, Problem 1E , additional homework tip 5

Figure (5)

Definitions:

Arc:

An arc XY(X→Y) 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.

Answer 43

Ch. 8 - For the digraph shown in Fig. 8-25, find a.the...Ch. 8 - For the digraph shown in Fig. 8-26, find Figure...Ch. 8 - For the digraph in Fig. 8-25, find a.all path of...Ch. 8 - For the digraph in Fig. 8-26, find a.a path of...Ch. 8 - For the digraph in Fig. 8-25, find a.all cycles of...Ch. 8 - For the digraph in Fig. 8-26, find a.all cycles of...Ch. 8 - Prob. 7E Ch. 8 - For the digraph in Fig.8-26, find a.all vertices...Ch. 8 - a.Draw a digraph with vertex-set V={A,B,C,D} and...Ch. 8 - a.Draw a digraph with vertex-set V={A,B,C,D} and...

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. Figure 8-25

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