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discrete math
a. Consider the following rooted tree: 7 10 11 12 i. What is the...
Discrete Math help. Draw the adjacency matrix for a graph . Figure out how many walks...
Discrete Math help. Draw the adjacency matrix for a graph . Figure out how many walks of length 2?
Let T_1 be the rooted tree consisting of a single root vertex. For n greaterthanorequalto 2,...
Let T_1 be the rooted tree consisting of a single root vertex. For n greaterthanorequalto 2, let T_n be the rooted tree consisting of a root vertex with four children, where the subtree rooted at each child is the tree T_n - 1. (a) Calculate how many paths in T_n start from the root vertex and end at a leaf vertex. (b) What is the minimum number of bits (0's and 1's) required to represent a path in T_n that...
Solve all parts please 5. In the following problems, recall that the adjacency matrix (or incidence matrix) for a simp...
Solve all parts please
5. In the following problems, recall that the adjacency matrix (or incidence matrix) for a simple graph with n vertices is an n x n matrix with entries that are all 0 or 1. The entries on the diagonal are all 0, and the entry in the ih row and jth column is 1 if there is an edge between vertex i and vertex j and is 0 if there is not an edge between vertex...
1. Consider the directed graph on the right side of the following page and complete the...
1. Consider the directed graph on the right side of the following page and complete the exercises below. When conducting a search, be very careful (since a small error early on can result in a large deduction of marks), and whenever you have a "choice" of which adjacent vertex to consider, you must consider the vertices in numerical order from least to greatest. (10 marks total) a. Provide an adjacency list representation of this graph. b. Compute the depth-first search...
Note that for the following question you should use technology to do the matrix calculations. Consider a graph with the following adjacency matrix: 0100 0 1 110011 0 01 0 11 00 0 11 1 01 1 10 0 Assum...
Note that for the following question you should use technology to do the matrix calculations. Consider a graph with the following adjacency matrix: 0100 0 1 110011 0 01 0 11 00 0 11 1 01 1 10 0 Assuming the nodes are labelled 1,2,3,4,5,6 in the same order as the rows and columns, answer the folllowing questions: (a) How many walks of length 2 are there from node 4 to itself? (b) How many walks of length 3 are...
Discrete Math: Please help with all parts of question 5. I have included problem 3 to...
Discrete Math: Please help with all parts of question
5. I have included problem 3 to help answer part (a) but
I only need help with question 5!
5.
3.
(a) (4 points) Prove that a graph is bipartite if and only if there is a 2-coloring (see problem 3) of its vertices. (b) (4 points) Prove that if a graph is a tree with at least two vertices, then there is a 2-coloring of its vertices. (Hint: Here are...
7. Graphs u, u2, u3, u4, u5, u6} and the (a) Consider the undirected graph G...
7. Graphs u, u2, u3, u4, u5, u6} and the (a) Consider the undirected graph G (V, E), with vertex set V set of edges E ((ul,u2), (u2,u3), (u3, u4), (u4, u5), (u5, u6). (u6, ul)} i. Draw a graphical representation of G. ii. Write the adjacency matrix of the graph G ii. Is the graph G isomorphic to any member of K, C, Wn or Q? Justify your answer. a. (1 Mark) (2 Marks) (2 Marks) b. Consider an...
math 270A quiz 10 discrete structures Name: Spring 2020 Math 270A Quiz 10 (MFCS 5.1-6.1) Directions:...
math 270A quiz 10 discrete structures
Name: Spring 2020 Math 270A Quiz 10 (MFCS 5.1-6.1) Directions: Please complete each question to the best of your ability. Show work to get full credit. Partially correct work will receive partial credit. Lastly please box your answer. 1. (2 points) Are the following graphs isomorphic? Explain why or why not. 2. (3 points) Find a minimum weight spanning tree of the graph below (either highlight the edges that make up the MST, or...
Help 2 2. II. Use the previous graphs to create the following: 1. Adjacency matrix for...
Help
2 2. II. Use the previous graphs to create the following: 1. Adjacency matrix for G in 1. 2. Incidence matrix for G in 1. 3. Adjacency list for G in 3. 4. Adjacency matrix for I in 5. 5. What is the degree of vertex a in 2. 6. If is a subgraph from G in 2. II-(K, L) is a complete graph, K-(b,c,d) and K C V. Draw the graph
Consider the following directed graph, which is given in adjacency list form and where vertexes have...
Consider the following directed graph, which is given in adjacency list form and where vertexes have numerical labels: 1: 2, 4, 6 2: 4, 5 3: 1, 2, 6, 9 4: 5 5: 4, 7 6: 1, 5, 7 7: 3, 5 8: 2, 6, 7 9: 1, 7 The first line indicates that the graph contains a directed edge from vertex 1 to vertex 2, from 1 to vertex 4, and 1 to 6, and likewise for subsequent lines....
Let T_1 be the rooted tree consisting of a single root vertex. For n greaterthanorequalto 2, let T_n be the rooted tree consisting of a root vertex with four children, where the subtree rooted at each child is the tree T_n - 1. (a) Calculate how many paths in T_n start from the root vertex and end at a leaf vertex. (b) What is the minimum number of bits (0's and 1's) required to represent a path in T_n that...
Solve all parts please
5. In the following problems, recall that the adjacency matrix (or incidence matrix) for a simple graph with n vertices is an n x n matrix with entries that are all 0 or 1. The entries on the diagonal are all 0, and the entry in the ih row and jth column is 1 if there is an edge between vertex i and vertex j and is 0 if there is not an edge between vertex...
1. Consider the directed graph on the right side of the following page and complete the exercises below. When conducting a search, be very careful (since a small error early on can result in a large deduction of marks), and whenever you have a "choice" of which adjacent vertex to consider, you must consider the vertices in numerical order from least to greatest. (10 marks total) a. Provide an adjacency list representation of this graph. b. Compute the depth-first search...
Note that for the following question you should use technology to do the matrix calculations. Consider a graph with the following adjacency matrix: 0100 0 1 110011 0 01 0 11 00 0 11 1 01 1 10 0 Assuming the nodes are labelled 1,2,3,4,5,6 in the same order as the rows and columns, answer the folllowing questions: (a) How many walks of length 2 are there from node 4 to itself? (b) How many walks of length 3 are...
Discrete Math: Please help with all parts of question
5. I have included problem 3 to help answer part (a) but
I only need help with question 5!
5.
3.
(a) (4 points) Prove that a graph is bipartite if and only if there is a 2-coloring (see problem 3) of its vertices. (b) (4 points) Prove that if a graph is a tree with at least two vertices, then there is a 2-coloring of its vertices. (Hint: Here are...
7. Graphs u, u2, u3, u4, u5, u6} and the (a) Consider the undirected graph G (V, E), with vertex set V set of edges E ((ul,u2), (u2,u3), (u3, u4), (u4, u5), (u5, u6). (u6, ul)} i. Draw a graphical representation of G. ii. Write the adjacency matrix of the graph G ii. Is the graph G isomorphic to any member of K, C, Wn or Q? Justify your answer. a. (1 Mark) (2 Marks) (2 Marks) b. Consider an...
math 270A quiz 10 discrete structures
Name: Spring 2020 Math 270A Quiz 10 (MFCS 5.1-6.1) Directions: Please complete each question to the best of your ability. Show work to get full credit. Partially correct work will receive partial credit. Lastly please box your answer. 1. (2 points) Are the following graphs isomorphic? Explain why or why not. 2. (3 points) Find a minimum weight spanning tree of the graph below (either highlight the edges that make up the MST, or...
Help
2 2. II. Use the previous graphs to create the following: 1. Adjacency matrix for G in 1. 2. Incidence matrix for G in 1. 3. Adjacency list for G in 3. 4. Adjacency matrix for I in 5. 5. What is the degree of vertex a in 2. 6. If is a subgraph from G in 2. II-(K, L) is a complete graph, K-(b,c,d) and K C V. Draw the graph
Consider the following directed graph, which is given in adjacency list form and where vertexes have numerical labels: 1: 2, 4, 6 2: 4, 5 3: 1, 2, 6, 9 4: 5 5: 4, 7 6: 1, 5, 7 7: 3, 5 8: 2, 6, 7 9: 1, 7 The first line indicates that the graph contains a directed edge from vertex 1 to vertex 2, from 1 to vertex 4, and 1 to 6, and likewise for subsequent lines....
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