To prove: When the algorithm terminates there is a path from vertex 1 to every other labeled vertex using only edges required by the algorithm.

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Answer 1

Question

Chapter 12.5, Problem 12E

(a)

To determine

To prove: When the algorithm terminates there is a path from vertex 1 to every other labeled vertex using only edges required by the algorithm.

(b)

To determine

To prove: If G is connected every vertex is labeled.

(c)

To determine

To prove: If G is connected then the vertices of G together with the edges used by the algorithm form a spanning tree.

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Determine whether each function is an injection and determine whether each is a surjection.The notation Z_(n) refers to the set {0,1,2,...,n-1}. For example, Z_(4)={0,1,2,3}. f: Z_(6) -> Z_(6) defined by f(x)=x^(2)+4(mod6). g: Z_(5) -> Z_(5) defined by g(x)=x^(2)-11(mod5). h: Z*Z -> Z defined by h(x,y)=x+2y. j: R-{3} -> R defined by j(x)=(4x)/(x-3).

Determine whether each function is an injection and determine whether each is a surjection.

Answer 2

Question

Chapter 12.5, Problem 12E

(a)

To determine

To prove: When the algorithm terminates there is a path from vertex 1 to every other labeled vertex using only edges required by the algorithm.

(b)

To determine

To prove: If G is connected every vertex is labeled.

(c)

To determine

To prove: If G is connected then the vertices of G together with the edges used by the algorithm form a spanning tree.

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Answer 3

Question

Chapter 12.5, Problem 12E

(a)

To determine

To prove: When the algorithm terminates there is a path from vertex 1 to every other labeled vertex using only edges required by the algorithm.

(b)

To determine

To prove: If G is connected every vertex is labeled.

(c)

To determine

To prove: If G is connected then the vertices of G together with the edges used by the algorithm form a spanning tree.

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Answer 4

Question

Chapter 12.5, Problem 12E

(a)

To determine

To prove: When the algorithm terminates there is a path from vertex 1 to every other labeled vertex using only edges required by the algorithm.

(b)

To determine

To prove: If G is connected every vertex is labeled.

(c)

To determine

To prove: If G is connected then the vertices of G together with the edges used by the algorithm form a spanning tree.

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Answer 5

Chapter 12.5, Problem 12E

(a)

To determine

To prove: When the algorithm terminates there is a path from vertex 1 to every other labeled vertex using only edges required by the algorithm.

(b)

To determine

To prove: If G is connected every vertex is labeled.

(c)

To determine

To prove: If G is connected then the vertices of G together with the edges used by the algorithm form a spanning tree.

Answer 6

Chapter 12.5, Problem 12E

(a)

To determine

To prove: When the algorithm terminates there is a path from vertex 1 to every other labeled vertex using only edges required by the algorithm.

Answer 7

Chapter 12.5, Problem 12E

(a)

To determine

To prove: When the algorithm terminates there is a path from vertex 1 to every other labeled vertex using only edges required by the algorithm.

Answer 8

(b)

To determine

To prove: If G is connected every vertex is labeled.

Answer 9

(b)

To determine

To prove: If G is connected every vertex is labeled.

Answer 10

(c)

To determine

To prove: If G is connected then the vertices of G together with the edges used by the algorithm form a spanning tree.

Answer 11

(c)

To determine

To prove: If G is connected then the vertices of G together with the edges used by the algorithm form a spanning tree.

Answer 12

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Answer 13

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Answer 14

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Answer 15

Ch. 12.1 - Prob. 1TFQ Ch. 12.1 - Prob. 2TFQ Ch. 12.1 - Prob. 3TFQ Ch. 12.1 - Prob. 4TFQ Ch. 12.1 - Prob. 5TFQ Ch. 12.1 - Prob. 6TFQ Ch. 12.1 - Prob. 7TFQ Ch. 12.1 - Prob. 8TFQ Ch. 12.1 - Prob. 9TFQ Ch. 12.1 - Prob. 10TFQ

To prove: When the algorithm terminates there is a path from vertex 1 to every other labeled vertex using only edges required by the algorithm.

Solution Summary: The author explains how the breadth-first search algorithm is applied to an arbitrary graph G.

To prove: When the algorithm terminates there is a path from vertex 1 to every other labeled vertex using only edges required by the algorithm.

To prove: If G is connected every vertex is labeled.

To prove: If G is connected then the vertices of G together with the edges used by the algorithm form a spanning tree.

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Chapter 12 Solutions