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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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…
In the following G, each adjacency list is sorted in increasing alphabetical order. B H Draw the component graph GSCC of G.
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An independent set in a graph G is a set S of vertices of G (so S is a subset of the vertex set V(G) of G) such that no two vertices from S are adjacent. A caterpillar is a tree T such that the graph obtained from T by removing all leaves is a path. Problem: Instance: a caterpillar T Problem: find the number of independent sets in T Design a recursive algorithm based on Divide and Conquer strategy for solving this problem. Prove its correctness. Estimate the time complexity of the algorithm.
9. The number of edges in a minimum spanning tree for a graph with V vertices and E edges is a) V-1. b) V. c) E-1. d) E. 10. Which of the following are a possible number of topological sort orderings for a directed acyclic graph with five vertices? a) 0 b) 1 c) 120 d) b and c e) all of the above
Draw a graph with the following conditions: 12 nodes total Directed, Acyclic Would have 4 possible options on the first iteration of topological sort
15 Consider the graph K3,3=G d if e Draw the following: a) G[ {a,b,d}] 6) G[{a, d, e, f3] c) G[{a,b,d,e}] d) G-{a} શે - { ,કે f) G-{a, d g) G-{c, d,e} h) G-{d, e, f} i) G-{a, c, e, f}
All lines of code in your program can be reached and executed when I run your program define two functions and they have a "meaningful purpose" to your program. Each function must have more than three statements or lines of code. At least one function defines a parameter and you use this parameter in a meaningful way At least one function returns a value back to the code that is calling it and it is used in a meaningful way
(V, E) be an undirected graph. Assume that the vertices 2. Let G represent documents. The edges are weighted so that w(i, j) is the dissimilarity between documents i and j. It is desired to partition the vertices into k > 3 disjoint clusters such that k ΣΣ υ(u, υ). i=1 (u,v)EE u,vEC; is minimized. The set C; is the set of documents in cluster i. Show that the e-approximate version of this problem is P-hard for all e, e > 0. Note that k is a fixed integer provided with each problem instance and may be different for different instances.
Please according to the following figure, which are right ? multiple choice
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Topic: GraphsSee attached photo for the problem

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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.