Given the following relation S, use ordered pair notation to express the relation So S.abсdS o S = { Ex: (a, b), (b, c)SHint: Start with a pair of vertices such as (a, b). If a can reach b by following two consecutive arrows in S, then(a, b) is in So S. Otherwise, (a, b) is not in So S.

Step 1: Step 2: Step 3: Step 4:

Answered: Given the following relation S, use…

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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Given the following relations S and U, use ordered pair notation to express the relation U o S. b S с a b U US={Ex: (a, b), (b, c) Hint: Start with a pair of vertices such as (a, b). If there exists some intermediate vertex that a can reach through one arrow in S and that intermediate vertex can reach b through one arrow in U, then (a, b) is in U o S. Otherwise, (a, b) is not in U o S.
Additional Topics: Topological Sort A strict order relation can be represented by a directed acyclic graph (or DAG), which is a directed graph with no cycles. For example, the following directed graph is a DAG: A topological sort of a DAG is an ordering of the vertices that is consistent with the edges of the graph. That is, if there is an edge (u, v) in the graph, then u should appear before v in the topological sort. For example, 1,2,3 and 1,3, 2 are topological sorts of the DAG shown above, but 2,1,3 is not a topological sort because 2 cannot be listed before 1. 7. Given the following DAG G representing UIC's Computer Science courses and prerequisites (note that edges implied by the transitive property are omitted): CS 261 CS 362 CS 141 CS 11 CS 211 Cs 361 CS 401 CS 151 CS 251 CS 342 Cs 301 Answer the following questions: a. Give two different topological sorts of G. b. Is each of the following orderings a topological sort of G? Justify your answer. CS111, CS151, CS301, CS251,…
Consider the following graph. 2 1) 4 Visually show how this graph will be saved in an adjacency matrix. Visually show how this graph will be saved in an adjacency list. Note: You only have to show the final adjacency matrix and adjacency list. No code required. 3.
26 Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider the following pair of graphs: X o1:02 48 V3 us V4 If the given graphs are isomorphic, then identify the correct mapping between the sets of vertices of the two graphs. Multiple Choice Aun) = v1, Au2) = v2, luz) = v3, fU4) = V5, and fu5) = v4 uiz Tools AU) = V, Au2) = v3, Auz) = v2, fu4) = V5, and fug) = v4 The two graphs are not isomorphic. 00% Aun) = V1, Au2) = V3, Auz) = v2, Au4) = v4, and flu5) = v5 se
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…
Assignment on Graph A social graph contains all the friendship relations (edges) among a group of n people (vertices). The friendship relationship is symmetric. Two vertices with no edge between them are enemies. Design and implement a class called Graph for a social graph. It should have an adjacency matrix as a data member to represent the graph. The nodes in the graph are numbered from 0..n-1 graph[i][i] - is always true (1) graph[i][j] is true if i and j are friends and false (0) if they are enemies. • In the constructor, initialize all entries to false (0) and all graph[i][i] to true (1) Include the following member functions. o void makeFriends(int i,intj)- make i and j friends int countFriends(int i) - will return the number of friends of i, excluding itself int countEnemies(int i)- will return the number of enemies of i int countCommonFriends(int i,intj) - the number of common friends of i and j int countCommonEnemies(int i,intj) - the number of common enemies of i and j int…
When a vertex Q is connected by an edge to a vertex K, what is the term for the relationship between Q and K? *a) Q and K are "insecure."b) Q and K are "incident."c) Q and K are "adjacent."d) Q and K are "isolated."
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…
Specifications: You will create an implementation of this algorithm. Your driver program should provide a graph and a source vertex in the graph. Your implementation should use Dijkstra's Algorithm to determine the shortest path using adjacency matrix representation. Specifically, given a graph and a source vertex in the graph, find the shortest paths from source to all vertices in the given graph, using Dijkstra's Algorithm.
Discrete Mathmatics The graph intersection of a collection of sets A1, A2, · · · , An is the graph that has a vertex for each of these sets and has an edge connecting the vertices representing two sets if these sets have a nonempty intersection. Construct the intersection graph for of the following collection of sets. A1 = {0, 2, 4, 6, 8} A2 = {0, 1, 2, 3, 4} A3 = {1, 3, 5, 7, 9} A4 = {5, 6, 7, 8, 9} A5 = {0, 1, 8, 9}
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color; this is called a vertex coloring. The chromatic number of a graph is the least mumber of colors required to do a coloring of a graph. Example Here in this graph the chromatic number is 3 since we used 3 colors The degree of a vertex v in a graph (without loops) is the number of edges at v. If there are loops at v each loop contributes 2 to the valence of v. A graph is connected if for any pair of vertices u and v one can get from u to v by moving along the edges of the graph. Such routes that move along edges are known by different names: edge progressions, paths, simple paths, walks, trails, circuits, cycles, etc. a. Write down the degree of the 16 vertices in the graph below: 14…
Question 11 Complete the function body below. def max_neighbours(g): Input : adjacency matrix of graph (g) Out put: vertex with maximum number of neighbours in g # your code here #

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Given the following relation S, use ordered pair notation to express the relation So S. a b с d S o S = { Ex: (a, b), (b, c) S Hint: Start with a pair of vertices such as (a, b). If a can reach b by following two consecutive arrows in S, then (a, b) is in So S. Otherwise, (a, b) is not in So S.