B D. E The Graph above shows how the execution of different tasks (represented by the vertices of the Graph) depend on the completion of other tasks. For example, prior to the starting of task D, tasks A and B need to be completed. You are required to find the linear ordering of the vertices such that if (u, v) is an edge, then u precedes v in the ordering. Show your working clearly.

B D. E The Graph above shows how the execution of different tasks (represented by the vertices of the Graph) depend on the completion of other tasks. For example, prior to the starting of task D, tasks A and B need to be completed. You are required to find the linear ordering of the vertices such that if (u, v) is an edge, then u precedes v in the ordering. Show your working clearly.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Undirected graph is given with the list of edges. Build an adjacency matrix. Print the number of ones in adjacency matrix. Graph can contain multiple edges and loops. Input First line contains number of vertices n. Each of the next line contains one edge. Read the edges till the end of file. Output Build an adjacency matrix. Print the number of ones in adjacency matrix. Sample input 3 1 2 23 22 32 Sample output 5
b) A D E The Graph above shows how the execution of different tasks (represented by the vertices of the Graph) depend on the completion of other tasks. For example, prior to the starting of task D, tasks A and B need to be completed. You are required to find the linear ordering of the vertices such that if (u, v) is an edge, then u precedes v in the ordering. Show your working clearly. B
If we need a lot of adding and removing edges to a graph, it is better to represent the graph as O Adjacency matrix O Adjacency list
1. Unreachable Nodes You have been given an undirected graph consisting of N nodes and Medges. The nodes in this graph are enumerated from 1 to N. The graph can consist of self-loops as well as multiple edges. This graph consists of a special node called the head node. You need to consider this and the entry point of this graph. You need to find the number of nodes that are unreachable from this head node. Create a function unreachableNodesCount (N, M, ListofEdges, HeadNode) where N is the number of nodes, M is the number of edges, List0fEdges contains list of edges in the graph and HeadNode is a special node which is the entry point of this graph. The function will return the number of nodes that are unreachable from the head node. Note: You will need to use N, M and List of Edges to first create the graph, as well as a search function to define the unreachable nodes count. >>>N = 10 >>> M = 10 >>> ListofEdges [(8, 1), (8, 3), (7, 4), (7, 5), (2, 6), (10, 7), (2, 8), (10, 9), (2, 10),…
5. (This question goes slightly beyond what was covered in the lectures, but you can solve it by combining algorithms that we have described.) A directed graph is said to be strongly connected if every vertex is reachable from every other vertex; i.e., for every pair of vertices u, v, there is a directed path from u to v and a directed path from v to u. A strong component of a graph is then a maximal subgraph that is strongly connected. That is all vertices in a strong component can reach each other, and any other vertex in the directed graph either cannot reach the strong component or cannot be reached from the component. (Note that we are considering directed graphs, so for a pair of vertices u and v there could be a path from u to v, but no path path from v back to u; in that case, u and v are not in the same strong component, even though they are connected by a path in one direction.) Given a vertex v in a directed graph D, design an algorithm for com- puting the strong connected…
The Graph Data Structure is made up of nodes and edges. (A Tree Data Structure is a special kind of a Graph Data Structure). A Graph may be represented by an Adjacency Matrix or an Adjacency List. Through this exercise, you should be able to have a better grasp the Adjacency Matrix concept. You are expected to read about the Adjacency Matrix concept as well as the Adjacency List concept. Suppose the vertices A, B, C, D, E, F, G and H of a Graph are mapped to row and column indices(0,1,2,3,4,5,6,and 7) of a matrix (i.e. 2-dimensional array) as shown in the following table. Vertex of Graph Index in the 2-D Array Adjacency Matrix Representation of Graph A B 2 F 6. H 7 Suppose further, that the following is an Adjacency Matrix representing the Graph. 3 4 5. 6. 7 0. 1 1 1 1 01 1 01 1. 3 14 1 1 1 6. 1 Exercise: Show/Draw the Graph that is represented by the above Adjacency matrix. Upload the document that contains your result. (Filename: AdjacencyMatrixExercise.pdf) Notes: -The nodes of the…
"For the undirected graph shown below, give the number of vertices, the number of edges, and the degree of each vertex, and represent the graph with an adjacency matrix." This task is solved here, but it is only solved for task a, not b. could you help me with task b?
Draw the graph represented by the following adjacency matrix on a piece of paper, take a photo of your work, and upload it here. Also, answer the following question about this graph: in what order do we visit the vertices if we run a BFS starting from vertex o? (vertices are labelled o to 3) 0011 1011 0101 1010
One can manually count path lengths in a graph using adjacency matrices. Using the simple example below, produces the following adjacency matrix: A B A 1 1 B 1 0 This matrix means that given two vertices A and B in the graph above, there is a connection from A back to itself, and a two-way connection from A to B. To count the number of paths of length one, or direct connections in the graph, all one must do is count the number of 1s in the graph, three in this case, represented in letter notation as AA, AB, and BA. AA means that the connection starts and ends at A, AB means it starts at A and ends at B, and so on. However, counting the number of two-hop paths is a little more involved. The possibilities are AAA, ABA, and BAB, AAB, and BAA, making a total of five 2-hop paths. The 3-hop paths starting from A would be AAAA, AAAB, AABA, ABAA, and ABAB. Starting from B, the 3-hop paths are BAAA, BAAB, and BABA. Altogether, that would be eight 3-hop paths within this graph. Write a program…
In the figure below there is a weighted graph, dots represent vertices, links represent edges, and numbers represent edge weights. S 2 1 2 1 2 3 T 1 1 2 4 (a) Find the shortest path from vertex S to vertex T, i.e., the path of minimum weight between S and T. (b) Find the minimum subgraph (set of edges) that connects all vertices in the graph and has the smallest total weight (sum of edge weights). 2. 3.
2. Use the following description of an undirected graph and draw the graph: v(Graph1) = { A, B, C, D} E(Graph1) = { (A,B), (A,D), (B,C), (B,D) }
Graph Transversal Simulation: For this graph write down the order of vertices encountered in a breadth-first search starting from vertex A. Break ties by picking the vertices in alphabetical order (for example, A before Z)