Homework Answers
Every vertex except the root is the child of an internal vertex. Because each of i internal vertex have m children there are mi vertices in the tree other than root. Hence the tree contains mi +1 vertices.
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Subject is Graph Theory
Problem 3. What is the maximum number of vertices (internal and leaves)...
Suppose that a full m-ary tree T has 109 vertices and height 2. (a) What are the possible values of m? (b) Assume also that T has at least 84 leaves. Now what are the possible values of m? (c) What v...
Suppose that a full m-ary tree T has 109 vertices and height 2. (a) What are the possible values of m? (b) Assume also that T has at least 84 leaves. Now what are the possible values of m? (c) What value of m maximizes the number of internal vertices in T? (d) For this value of m identify the number of leaves and number of internal vertices at each level of T.
How many leaves and internal vertices does a full 5 - ary tree have with 401 total vertices?
How many leaves and internal vertices does a full 5 - ary tree have with 401 total vertices?
suppose that a full 4-ary tree has 100 leaves. howmany internal vertices does it have? please...
suppose that a full 4-ary tree has 100 leaves. howmany internal vertices does it have? please explain in detail. i dont want to know about no. of vertices i just need to find internal vertices . can you also explain how is 4 ary tree look alike.? thanks,
How many leaves does a full 3-ary tree with 100 vertices have?
How many leaves does a full 3-ary tree with 100 vertices have?
What is the maximum possible number of edges in a graph with n vertices if: (a)...
What is the maximum possible number of edges in a graph with n vertices if: (a) the graph is simple? (b) the graph is acyclic? (c) the graph is planar? Try to justify your answers. [Hint: first look at graphs with few vertices.] Need a clear answer with good neat handwriting please.
4. Given a commected weighted directed graph with n vertices, what is the maximum mumber of possible tours in the T...
4. Given a commected weighted directed graph with n vertices, what is the maximum mumber of possible tours in the Traveling Salesman Problem? 5. In the n-Queens problem as given in the textbook, where it is assumed that no two queens can occupy the same row on annx n chessboard, how many nodes are there in the total stat space tree without pruning? 6. As in the previous question, how many leaf nodes in the state space tree? z2 7....
3. Find a graph with the given set of properties or explain why no such graph...
3. Find a graph with the given set of properties or explain why no such graph can exist. The graphs do not need to be trees unless explicitly stated. (a) tree, 7 vertices, total degree = 12. (b) connected, no multi-edges, 5 vertices, 11 edges. (c) tree, all vertices have degree <3, 6 leaves, 4 internal vertices. (d) connected, five vertices, all vertices have degree 3.
Recall the definition of the degree of a vertex in a graph. a) Suppose a graph has 7 vertices, each of degree 2 or 3. Is the graph necessarily connected ? b) Now the graph has 7 vertices, each degree...
Recall the definition of the degree of a vertex in a graph. a)
Suppose a graph has 7 vertices, each of degree 2 or 3. Is the graph
necessarily connected ?
b) Now the graph has 7 vertices, each degree 3 or 4. Is it
necessarily connected?
My professor gave an example in class. He said triangle and a
square are graph which are not connected yet each vertex has degree
2.
(Paul Zeitz, The Art and Craft of Problem...
Answer each question in the space provided below. 1. Draw all non-isomorphic free trees with five...
Answer each question in the space provided below. 1. Draw all non-isomorphic free trees with five vertices. You should not include two trees that are isomorphic. 2. If a tree has n vertices, what is the maximum possible number of leaves? (Your answer should be an expression depending on the variable n. 3. Find a graph with the given set of properties or explain why no such graph can exist. The graphs do not need to be trees unless explicitly...
3. A Unicvcle Problem Prove that a cycle exists in an undirected graph if and only...
3. A Unicvcle Problem Prove that a cycle exists in an undirected graph if and only if a BFS of that graph has a cross-edge. (**) Your proof may use the following facts from graph theory . There exists a unique path between any two vertices of a tree. . Adding any edge to a tree creates a unique cycle.
4. Given a commected weighted directed graph with n vertices, what is the maximum mumber of possible tours in the Traveling Salesman Problem? 5. In the n-Queens problem as given in the textbook, where it is assumed that no two queens can occupy the same row on annx n chessboard, how many nodes are there in the total stat space tree without pruning? 6. As in the previous question, how many leaf nodes in the state space tree? z2 7....
3. Find a graph with the given set of properties or explain why no such graph can exist. The graphs do not need to be trees unless explicitly stated. (a) tree, 7 vertices, total degree = 12. (b) connected, no multi-edges, 5 vertices, 11 edges. (c) tree, all vertices have degree <3, 6 leaves, 4 internal vertices. (d) connected, five vertices, all vertices have degree 3.
Recall the definition of the degree of a vertex in a graph. a)
Suppose a graph has 7 vertices, each of degree 2 or 3. Is the graph
necessarily connected ?
b) Now the graph has 7 vertices, each degree 3 or 4. Is it
necessarily connected?
My professor gave an example in class. He said triangle and a
square are graph which are not connected yet each vertex has degree
2.
(Paul Zeitz, The Art and Craft of Problem...
Answer each question in the space provided below. 1. Draw all non-isomorphic free trees with five vertices. You should not include two trees that are isomorphic. 2. If a tree has n vertices, what is the maximum possible number of leaves? (Your answer should be an expression depending on the variable n. 3. Find a graph with the given set of properties or explain why no such graph can exist. The graphs do not need to be trees unless explicitly...
3. A Unicvcle Problem Prove that a cycle exists in an undirected graph if and only if a BFS of that graph has a cross-edge. (**) Your proof may use the following facts from graph theory . There exists a unique path between any two vertices of a tree. . Adding any edge to a tree creates a unique cycle.
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