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Consider a 4-ary tree T consisting of 17 vertices. What is the sum of the degree of T?
Correct answer is '32'. Can you explain this answer?
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Consider a 4-ary tree T consisting of 17 vertices. What is the sum of ...
Concept:
By using handshaking theorem of graph theory, the sum of degree of all the vertices in a tree is equal to twice the number of edges in a graph.
By using handshaking theorem of graph theory, the sum of degree of all the vertices in a tree is equal to twice the number of edges in a graph.
Formula:
where di is the degree of vertex i and e is the total number of edges in a graph
where di is the degree of vertex i and e is the total number of edges in a graph
Calculation:
For a tree,
number of edges = e = n – 1
sum of the degrees of all the vertices in T is 32.
For a tree,
number of edges = e = n – 1
sum of the degrees of all the vertices in T is 32.
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Consider a 4-ary tree T consisting of 17 vertices. What is the sum of ...
Sum of the degrees of a tree:
In a tree, the sum of the degrees of all vertices is equal to twice the number of edges. This is because each edge connects two vertices, contributing degree 1 to each vertex. Therefore, the sum of the degrees of all vertices is twice the number of edges.
Given information:
We are given a 4-ary tree T consisting of 17 vertices. A 4-ary tree is a tree in which each vertex can have up to 4 children.
Finding the number of edges:
To find the number of edges in the tree, we can use the formula:
number of edges = (number of vertices - 1)
Applying this formula to the given tree, we have:
number of edges = 17 - 1 = 16
Calculating the sum of the degrees:
Using the formula mentioned earlier, the sum of the degrees of the tree is:
sum of degrees = 2 * number of edges
substituting the value of the number of edges, we get:
sum of degrees = 2 * 16 = 32
Therefore, the sum of the degree of the given 4-ary tree T is 32.
Conclusion:
The sum of the degrees of a tree is equal to twice the number of edges. In the given 4-ary tree T consisting of 17 vertices, the number of edges is 16. Therefore, the sum of the degrees is 32.
In a tree, the sum of the degrees of all vertices is equal to twice the number of edges. This is because each edge connects two vertices, contributing degree 1 to each vertex. Therefore, the sum of the degrees of all vertices is twice the number of edges.
Given information:
We are given a 4-ary tree T consisting of 17 vertices. A 4-ary tree is a tree in which each vertex can have up to 4 children.
Finding the number of edges:
To find the number of edges in the tree, we can use the formula:
number of edges = (number of vertices - 1)
Applying this formula to the given tree, we have:
number of edges = 17 - 1 = 16
Calculating the sum of the degrees:
Using the formula mentioned earlier, the sum of the degrees of the tree is:
sum of degrees = 2 * number of edges
substituting the value of the number of edges, we get:
sum of degrees = 2 * 16 = 32
Therefore, the sum of the degree of the given 4-ary tree T is 32.
Conclusion:
The sum of the degrees of a tree is equal to twice the number of edges. In the given 4-ary tree T consisting of 17 vertices, the number of edges is 16. Therefore, the sum of the degrees is 32.
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Consider a 4-ary tree T consisting of 17 vertices. What is the sum of the degree of T?Correct answer is '32'. Can you explain this answer?
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Consider a 4-ary tree T consisting of 17 vertices. What is the sum of the degree of T?Correct answer is '32'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Consider a 4-ary tree T consisting of 17 vertices. What is the sum of the degree of T?Correct answer is '32'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a 4-ary tree T consisting of 17 vertices. What is the sum of the degree of T?Correct answer is '32'. Can you explain this answer?.
Consider a 4-ary tree T consisting of 17 vertices. What is the sum of the degree of T?Correct answer is '32'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Consider a 4-ary tree T consisting of 17 vertices. What is the sum of the degree of T?Correct answer is '32'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a 4-ary tree T consisting of 17 vertices. What is the sum of the degree of T?Correct answer is '32'. Can you explain this answer?.
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