(a) To find: All the vertices that are incident to A using given digraph.

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Answer 1

Question

Chapter 8, Problem 7E

To determine

(a)

To find:

All the vertices that are incident to A using given digraph.

To determine

(b)

To find:

All the vertices that are incident from A using given digraph.

To determine

(c)

To find:

All the vertices that are incident to D using given digraph.

To determine

(d)

To find:

All the vertices that are incident from D using given digraph.

To determine

(e)

To find:

All the arcs adjacent to AC using given digraph.

To determine

(f)

To find:

All the arcs adjacent to CD using given digraph.

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By considering appropriate series expansions, e². e²²/2. e²³/3. .... = = 1 + x + x² + · ... when |x| < 1. By expanding each individual exponential term on the left-hand side the coefficient of x- 19 has the form and multiplying out, 1/19!1/19+r/s, where 19 does not divide s. Deduce that 18! 1 (mod 19).

Proof: LN⎯⎯⎯⎯⎯LN¯ divides quadrilateral KLMN into two triangles. The sum of the angle measures in each triangle is ˚, so the sum of the angle measures for both triangles is ˚. So, m∠K+m∠L+m∠M+m∠N=m∠K+m∠L+m∠M+m∠N=˚. Because ∠K≅∠M∠K≅∠M and ∠N≅∠L, m∠K=m∠M∠N≅∠L, m∠K=m∠M and m∠N=m∠Lm∠N=m∠L by the definition of congruence. By the Substitution Property of Equality, m∠K+m∠L+m∠K+m∠L=m∠K+m∠L+m∠K+m∠L=°,°, so (m∠K)+ m∠K+ (m∠L)= m∠L= ˚. Dividing each side by gives m∠K+m∠L=m∠K+m∠L= °.°. The consecutive angles are supplementary, so KN⎯⎯⎯⎯⎯⎯∥LM⎯⎯⎯⎯⎯⎯KN¯∥LM¯ by the Converse of the Consecutive Interior Angles Theorem. Likewise, (m∠K)+m∠K+ (m∠N)=m∠N= ˚, or m∠K+m∠N=m∠K+m∠N= ˚. So these consecutive angles are supplementary and KL⎯⎯⎯⎯⎯∥NM⎯⎯⎯⎯⎯⎯KL¯∥NM¯ by the Converse of the Consecutive Interior Angles Theorem. Opposite sides are parallel, so quadrilateral KLMN is a parallelogram.

By considering appropriate series expansions, ex · ex²/2 . ¸²³/³ . . .. = = 1 + x + x² +…… when |x| < 1. By expanding each individual exponential term on the left-hand side and multiplying out, show that the coefficient of x 19 has the form 1/19!+1/19+r/s, where 19 does not divide s.

Answer 2

Question

Chapter 8, Problem 7E

To determine

(a)

To find:

All the vertices that are incident to A using given digraph.

To determine

(b)

To find:

All the vertices that are incident from A using given digraph.

To determine

(c)

To find:

All the vertices that are incident to D using given digraph.

To determine

(d)

To find:

All the vertices that are incident from D using given digraph.

To determine

(e)

To find:

All the arcs adjacent to AC using given digraph.

To determine

(f)

To find:

All the arcs adjacent to CD using given digraph.

Expert Solution & Answer

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See solution

Answer 3

Question

Chapter 8, Problem 7E

To determine

(a)

To find:

All the vertices that are incident to A using given digraph.

To determine

(b)

To find:

All the vertices that are incident from A using given digraph.

To determine

(c)

To find:

All the vertices that are incident to D using given digraph.

To determine

(d)

To find:

All the vertices that are incident from D using given digraph.

To determine

(e)

To find:

All the arcs adjacent to AC using given digraph.

To determine

(f)

To find:

All the arcs adjacent to CD using given digraph.

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Answer 4

Question

Chapter 8, Problem 7E

To determine

(a)

To find:

All the vertices that are incident to A using given digraph.

To determine

(b)

To find:

All the vertices that are incident from A using given digraph.

To determine

(c)

To find:

All the vertices that are incident to D using given digraph.

To determine

(d)

To find:

All the vertices that are incident from D using given digraph.

To determine

(e)

To find:

All the arcs adjacent to AC using given digraph.

To determine

(f)

To find:

All the arcs adjacent to CD using given digraph.

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Answer 5

Chapter 8, Problem 7E

To determine

(a)

To find:

All the vertices that are incident to A using given digraph.

To determine

(b)

To find:

All the vertices that are incident from A using given digraph.

To determine

(c)

To find:

All the vertices that are incident to D using given digraph.

To determine

(d)

To find:

All the vertices that are incident from D using given digraph.

To determine

(e)

To find:

All the arcs adjacent to AC using given digraph.

To determine

(f)

To find:

All the arcs adjacent to CD using given digraph.

Answer 6

Chapter 8, Problem 7E

To determine

(a)

To find:

All the vertices that are incident to A using given digraph.

Answer 7

Chapter 8, Problem 7E

To determine

(a)

To find:

All the vertices that are incident to A using given digraph.

Answer 8

To determine

(b)

To find:

All the vertices that are incident from A using given digraph.

Answer 9

To determine

(b)

To find:

All the vertices that are incident from A using given digraph.

Answer 10

To determine

(c)

To find:

All the vertices that are incident to D using given digraph.

Answer 11

To determine

(c)

To find:

All the vertices that are incident to D using given digraph.

Answer 12

To determine

(d)

To find:

All the vertices that are incident from D using given digraph.

Answer 13

To determine

(d)

To find:

All the vertices that are incident from D using given digraph.

Answer 14

To determine

(e)

To find:

All the arcs adjacent to AC using given digraph.

Answer 15

To determine

(e)

To find:

All the arcs adjacent to AC using given digraph.

Answer 16

To determine

(f)

To find:

All the arcs adjacent to CD using given digraph.

Answer 17

To determine

(f)

To find:

All the arcs adjacent to CD using given digraph.

Answer 18

Expert Solution & Answer

Answer 19

Expert Solution & Answer

Answer 20

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Answer 21

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...

(a) To find: All the vertices that are incident to A using given digraph.

Solution Summary: The vertices that are incident to A are B, C, and E.

(a)

To find:

All the vertices that are incident to A using given digraph.

(b)

To find:

All the vertices that are incident from A using given digraph.

(c)

To find:

All the vertices that are incident to D using given digraph.

(d)

To find:

All the vertices that are incident from D using given digraph.

(e)

To find:

All the arcs adjacent to AC using given digraph.

(f)

To find:

All the arcs adjacent to CD using given digraph.

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Chapter 8 Solutions

(a) To find: All the vertices that are incident to A using given digraph.

Solution Summary: The vertices that are incident to A are B, C, and E.

(a) To find: All the vertices that are incident to A using given digraph.

(b) To find: All the vertices that are incident from A using given digraph.

(c) To find: All the vertices that are incident to D using given digraph.

(d) To find: All the vertices that are incident from D using given digraph.

(e) To find: All the arcs adjacent to AC using given digraph.

(f) To find: All the arcs adjacent to CD using given digraph.

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Chapter 8 Solutions

(a)

To find:

All the vertices that are incident to A using given digraph.

(b)

To find:

All the vertices that are incident from A using given digraph.

(c)

To find:

All the vertices that are incident to D using given digraph.

(d)

To find:

All the vertices that are incident from D using given digraph.

(e)

To find:

All the arcs adjacent to AC using given digraph.

(f)

To find:

All the arcs adjacent to CD using given digraph.