Homework Answers
In case we are given a directed graph with n vertices. Then we construct an n × n adjacency matrix A associated to the graph as follows: if there is an edge from node i to node j, then we put 1 as the entry on row i, column j of the matrix A else it remains 0.
I ) matrix is
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 |
2)incidence matrix is plotted for vertices against edges .the value of a vertices against an edge is one if it is coming towards the current vertex from any other edge while it is -1 if it is moving towards any other vertex from the current vertex.hence the incidence matrix is shown in the image below.
3)the solution for the current question is given in the image below.
4)question missing.
5)the degree of a vertex in a graph is the (no of incoming edges from the vertex + no of outgoing edges from the vertex ). hence the degree of vertex a in 2 is 3.
6)the solution of given question is shown in image below.The graph is complete and also sub graph of the graph shown in figure 2 with only b,c and d vertices.
hope this helps !
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2 2. II. Use the previous graphs to create the following: 1. Adjacency matrix for...
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...
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...
Please answer question 2. Introduction to Trees Thank you 1. Graphs (11 points) (1) (3 points)...
Please answer question 2. Introduction to Trees
Thank you
1. Graphs (11 points) (1) (3 points) How many strongly connected components are in the three graphs below? List the vertices associated with each one. 00 (2) (4 points) For the graph G5: (a) (0.5 points) Specify the set of vertices V. (b) (0.5 points) Specify the set of edges E. (c) (1 point) Give the degree for each vertex. (d) (1 point) Give the adjacency matrix representation for this graph....
Task 3: Grid Graphs and Mazes Part A - Generating Grid Graphs In the lecture we...
Task 3: Grid Graphs and Mazes Part A - Generating Grid Graphs In the lecture we said that we can use Prim's algorithm to create mazes by starting from a regular "grid graph and then finding a spanning tree. Implement a function grid graph (m, n) that takes as input two positive integers, and returns the adjacency matrix of a m by n grid graphie, a graph with ses vertices that, when drawn on a regular m by n grid,...
I need help to solve this. A5CompanyA.txt A5CompanyB.txt continues this are tables 13.3 and 13.4 Question...
I need help to solve this.
A5CompanyA.txt
A5CompanyB.txt
continues
this are tables 13.3 and 13.4
Question 1: Graphs This question is similar to the question seen in Exercise 5. It is recommended that you complete Exercise 5 prior to attempting this question. For each of the two graphs given below, complete the following four items. No code is required for this question. 1. Draw the graph corresponding to the given adjaceney matrix (graph 1) or adjacency list (graph 2). 2....
4&5 0 1 2 3 1. Draw the undirected graph that corresponds to this adjacency matrix...
4&5
0 1 2 3 1. Draw the undirected graph that corresponds to this adjacency matrix 0 0 1 1 0 1 1 1 1 0 1 1 1 2 1 1 1 0 1 3 1 0 1 1 0 1 2. Given the following directed graph, how would you represent it with an adjacency list? 3. We've seen two ways to store graphs - adjacency matrices, and adjacency lists. For a directed graph like the one shown above,...
8, (10 pts) Show that given a directed graph G = (V,E) already stored in adjacency matrix form, determining if there is a vertex with in-degree n - 1 and out-degree 0 can be done in O(n) time whe...
8, (10 pts) Show that given a directed graph G = (V,E) already stored in adjacency matrix form, determining if there is a vertex with in-degree n - 1 and out-degree 0 can be done in O(n) time where n is the number of vertices in V.
8, (10 pts) Show that given a directed graph G = (V,E) already stored in adjacency matrix form, determining if there is a vertex with in-degree n - 1 and out-degree 0 can...
Hello, I'd like someone to help me create these, thanks! 1. Type Vertex Create and document...
Hello, I'd like someone to help me create these, thanks! 1. Type Vertex Create and document type Vertex. Each vertex v has the following pieces of information. A pointer to a linked list of edges listing all edges that are incident on v. This list is called an adjacency list. A real number indicating v's shortest distance from the start vertex. This number is −1 if the distance is not yet known. A vertex number u. The shortest path from...
Please answer A and B 1. Consider the following adjacency matrix representing vertices v through v^:...
Please answer A and B
1. Consider the following adjacency matrix representing vertices v through v^: weighted graph containing a ro 5 0 0 8 0 61 5 0 0 7 0 0 0 jo 0 0 0 0 1 3| 0 7 0 0 2 0 0 8 0 0 0 0 1 0 0 0 4 L6 0 3 0 0 4 0- 20 0 0 a. Draw the graph resulting from the adjacency matrix b. Assuming the...
G1: I can create a graph given information or rules about vertices and edges. I can...
G1: I can create a graph given information or rules about vertices and edges. I can give examples of graphs having combinations of various properties and examples of graphs of special (" named”) types. 1. Draw a graph G with • V(G) = {a,b,c,d,e,f}, • deg(d) = 2, • a and f are neighbors, • {b,d} & E(G), G is simple, • K4 is a subgraph of G. 2. Draw the graph C7. 3. Answer each question about the graph...
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...
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...
Please answer question 2. Introduction to Trees
Thank you
1. Graphs (11 points) (1) (3 points) How many strongly connected components are in the three graphs below? List the vertices associated with each one. 00 (2) (4 points) For the graph G5: (a) (0.5 points) Specify the set of vertices V. (b) (0.5 points) Specify the set of edges E. (c) (1 point) Give the degree for each vertex. (d) (1 point) Give the adjacency matrix representation for this graph....
Task 3: Grid Graphs and Mazes Part A - Generating Grid Graphs In the lecture we said that we can use Prim's algorithm to create mazes by starting from a regular "grid graph and then finding a spanning tree. Implement a function grid graph (m, n) that takes as input two positive integers, and returns the adjacency matrix of a m by n grid graphie, a graph with ses vertices that, when drawn on a regular m by n grid,...
I need help to solve this.
A5CompanyA.txt
A5CompanyB.txt
continues
this are tables 13.3 and 13.4
Question 1: Graphs This question is similar to the question seen in Exercise 5. It is recommended that you complete Exercise 5 prior to attempting this question. For each of the two graphs given below, complete the following four items. No code is required for this question. 1. Draw the graph corresponding to the given adjaceney matrix (graph 1) or adjacency list (graph 2). 2....
4&5
0 1 2 3 1. Draw the undirected graph that corresponds to this adjacency matrix 0 0 1 1 0 1 1 1 1 0 1 1 1 2 1 1 1 0 1 3 1 0 1 1 0 1 2. Given the following directed graph, how would you represent it with an adjacency list? 3. We've seen two ways to store graphs - adjacency matrices, and adjacency lists. For a directed graph like the one shown above,...
8, (10 pts) Show that given a directed graph G = (V,E) already stored in adjacency matrix form, determining if there is a vertex with in-degree n - 1 and out-degree 0 can be done in O(n) time where n is the number of vertices in V.
8, (10 pts) Show that given a directed graph G = (V,E) already stored in adjacency matrix form, determining if there is a vertex with in-degree n - 1 and out-degree 0 can...
Please answer A and B
1. Consider the following adjacency matrix representing vertices v through v^: weighted graph containing a ro 5 0 0 8 0 61 5 0 0 7 0 0 0 jo 0 0 0 0 1 3| 0 7 0 0 2 0 0 8 0 0 0 0 1 0 0 0 4 L6 0 3 0 0 4 0- 20 0 0 a. Draw the graph resulting from the adjacency matrix b. Assuming the...
G1: I can create a graph given information or rules about vertices and edges. I can give examples of graphs having combinations of various properties and examples of graphs of special (" named”) types. 1. Draw a graph G with • V(G) = {a,b,c,d,e,f}, • deg(d) = 2, • a and f are neighbors, • {b,d} & E(G), G is simple, • K4 is a subgraph of G. 2. Draw the graph C7. 3. Answer each question about the graph...
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