The number of vertices of degree 2. If a tree has 100 vertices of degree 1 and 20 of degree 6 and that one-half of the remaining vertices are degree 4 and the rest of degree 2.

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Answer 1

Question

Chapter 12.1, Problem 13E

To determine

The number of vertices of degree 2. If a tree has 100 vertices of degree 1 and 20 of degree 6 and that one-half of the remaining vertices are degree 4 and the rest of degree 2.

To determine

To prove: A tree has the vertices of degree 1 must be less than 80 cannot exist except as specified in part (a).

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(b) A planar graph has 10 edges and its dual graph has j edges, for some integer j. What is this j? Answer: j =

(a) Is there an undirected graph with 7 vertices such that five of the vertices have degree 3 and the remaining two have degree 4? If yes, then draw the graph and if not, then prove your answer. In the following, let T denote a full 3-ary (rooted) tree with 25 vertices. Justify your answers co the questions below. (b) Find the number of internal vertices (denote it by i) and the number of leaves of T (denote it by l). (c) What is the minimum possible height for T? (d) If T is balanced, then what is the height of T?

(a) Is there an undirected graph with 7 vertices such that five of the vertices have degree 3 and the remaining two have degree 4? If yes, then draw the graph and if not, then prove your answer. In the following, let T denote a full 3-ary (rooted) tree with 25 vertices. Justify your answers to the questions below. (b) Find the number of internal vertices (denote it by i) and the number of leaves of T (denote it by l). (c) What is the minimum possible height for T? (d) If T is balanced, then what is the height of T?

Answer 2

Question

Chapter 12.1, Problem 13E

To determine

The number of vertices of degree 2. If a tree has 100 vertices of degree 1 and 20 of degree 6 and that one-half of the remaining vertices are degree 4 and the rest of degree 2.

To determine

To prove: A tree has the vertices of degree 1 must be less than 80 cannot exist except as specified in part (a).

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Answer 3

Question

Chapter 12.1, Problem 13E

To determine

The number of vertices of degree 2. If a tree has 100 vertices of degree 1 and 20 of degree 6 and that one-half of the remaining vertices are degree 4 and the rest of degree 2.

To determine

To prove: A tree has the vertices of degree 1 must be less than 80 cannot exist except as specified in part (a).

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Answer 4

Question

Chapter 12.1, Problem 13E

To determine

The number of vertices of degree 2. If a tree has 100 vertices of degree 1 and 20 of degree 6 and that one-half of the remaining vertices are degree 4 and the rest of degree 2.

To determine

To prove: A tree has the vertices of degree 1 must be less than 80 cannot exist except as specified in part (a).

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Answer 5

Chapter 12.1, Problem 13E

To determine

The number of vertices of degree 2. If a tree has 100 vertices of degree 1 and 20 of degree 6 and that one-half of the remaining vertices are degree 4 and the rest of degree 2.

To determine

To prove: A tree has the vertices of degree 1 must be less than 80 cannot exist except as specified in part (a).

Answer 6

Chapter 12.1, Problem 13E

To determine

The number of vertices of degree 2. If a tree has 100 vertices of degree 1 and 20 of degree 6 and that one-half of the remaining vertices are degree 4 and the rest of degree 2.

Answer 7

Chapter 12.1, Problem 13E

To determine

The number of vertices of degree 2. If a tree has 100 vertices of degree 1 and 20 of degree 6 and that one-half of the remaining vertices are degree 4 and the rest of degree 2.

Answer 8

To determine

To prove: A tree has the vertices of degree 1 must be less than 80 cannot exist except as specified in part (a).

Answer 9

To determine

To prove: A tree has the vertices of degree 1 must be less than 80 cannot exist except as specified in part (a).

Answer 10

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Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

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

The number of vertices of degree 2. If a tree has 100 vertices of degree 1 and 20 of degree 6 and that one-half of the remaining vertices are degree 4 and the rest of degree 2.

Solution Summary: The author explains that if a tree has 100 vertices of degree 1 and 20, one-half of them are degree 4 and the rest is degree 2.

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The number of vertices of degree 2. If a tree has 100 vertices of degree 1 and 20 of degree 6 and that one-half of the remaining vertices are degree 4 and the rest of degree 2.

To prove: A tree has the vertices of degree 1 must be less than 80 cannot exist except as specified in part (a).

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Chapter 12 Solutions