IncorrectQuestion 9From a directed graph G, we can detect three strongly connected components (SCC),named as C1, C2, and C3. Which one(s) of the following statements are alwayscorrect?(1) If we perform depth-first (DFS) algorithm only inside C1, i.e. DFS(C1), there alwaysexists back edge in C1.(2) If we perform depth-first (DFS) algorithm in the whole graph G, the in-betweenedge (x, y) [where x is from C1, and y is from C2] must be a cross edge.(3) Procedure DFS(G) will finally generate three trees in the depth-first forest.(4) Any edges in-between C1 and C2, C2 and C3, C1 and C3 cannot form bigloops/cycles.(5) In the SCC graph, there might be multiple paths connecting from C1 to C2, butthey need to be in the same direction.O (1)(2)(3)(4)(5)

A directed graph is strongly connected if there is a path between all pairs of vertices. A strongly…

Answered: From a directed graph G, we can detect…

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

See similar textbooks

Similar questions

Given a graph that is a tree (connected and acyclic). (I) Pick any vertex v.(II) Compute the shortest path from v to every other vertex. Let w be the vertex with the largest shortest path distance.(III) Compute the shortest path from w to every other vertex. Let x be the vertex with the largest shortest path distance. Consider the path p from w to x. Which of the following are truea. p is the longest path in the graphb. p is the shortest path in the graphc. p can be calculated in time linear in the number of edges/vertices
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…
Given a graph that is a tree (connected and acyclic). (1) Pick any vertex v. (II) Compute the shortest path from v to every other vertex. Let w be the vertex with the largest shortest path distance. (III) Compute the shortest path from w to every other vertex. Let x be the vertex with the largest shortest path distance. Consider the path p from w to x. Which of the following are true a. p is the longest path in the graph b. p is the shortest path in the graph c. p can be calculated in time linear in the number of edges/vertices a,c a,b a,b,c b.c
Hamilton cycle A loop in the connected graph G=(V,E) passes through each vertex in the graph and only once. A Hamiltonian is a path (v,v,.V,.) starting from a certain node v, and looping along the n sides of the graph G. > Except for v,=v, the remaining nodes on the path are different. > (v,V.) EE (0si
Markup the BFS code so that it can determine if the graph g is connected or not. Further modify the BFS code so that that it is possible to determine the number of connected components and their membership (i.e., which vertices belong to which component). // Connectivity Checker and Identifier public static Integer[] ProcessOrderInBFS(Graph g) { int foundCount = 1; Integer[] processOrder = new Integer[g.size(O]; for (int i = 0; i q = new LinkedList(); int currNode = 0; Integer[] adjVector = null; q. add(startVertex); processorder[startVertex] = foundCount; foundCount++; while(!q.isEmpty()) { currNode = q.remove(); adjVector = g.getAdjVector(currNode); for (int i = 0; i < g.size(); i++) { if(adjVector[i] == 1 && processOrder[i] == 0) { q. add(i); processorder[i] = foundCount; foundCount++; } } } return foundCount;
B D F. E G H Suppose we run the Floyd-Warshall transitive closure algorithm on this graph. What is one edge that will be added in the first pass, paths through A? (For an edge from A to B, for example, you would write AB. If there is none, write NONE.) | What is one edge that will be added in the second pass? What is one edge that will be added in the third pass? What is the runtime of Floyd-Warshall on a graph with N vertices and M edges?
Starting with the tic-tac-toe program of Figure 12.4, draw a directed acyclic graph in which every clause is a node and an arc from A to B indicates that it is important, either for correctness or efficiency, that A come before B in the program. (Do not draw any other arcs.) Any topological sort of your graph should constitute an equally efficient version of the program. (Is the existing program one of them?)
Create a graph containing the following edges and display the nodes of a graph in depth first traversal and breadth first traversal. V(G) = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} E(G) = {(0, 1), (0, 5), (1, 2), (1, 3), (1, 5), (2, 4), (4, 3), (5, 6), (6, 8), (7, 3), (7, 8), (8, 10), (9, 4), (9, 7), (9, 10)} The input file should consist of the number of vertices in the graph in the first line and the vertices that are adjacent to the vertex in the following lines. Header File #ifndef H_graph #define H_graph #include <iostream> #include <fstream> #include <iomanip> #include "linkedList.h" #include "unorderedLinkedList.h" #include "linkedQueue.h" using namespace std; class graphType { public: bool isEmpty() const; void createGraph(); void clearGraph(); void printGraph() const; void depthFirstTraversal(); void dftAtVertex(int vertex); void breadthFirstTraversal(); graphType(int size = 0); ~graphType(); protected: int maxSize; //maximum number of…
Consider the graph in the figure below. E B F G AZ. с I H A a) List all the bridges in this graph. Enter your answers in alphabetical order separated by commas but no spaces. b) If you remove all of the bridges from this graph, how many components will the resulting graph have? c) What is the length of the shortest path from C to F? Length: 2 d) What is the length of the longest path from I to J? Length: 5 Check J ✔Path: C,I,F Path: I,G,F,I,H,J X X
Q3. Find the DFS and BFS for the following directed graph.(Start from 0) 2 3 4 5 6 8 04 Fznloin Mastor Thoorom Uging Mostor Thoorom solvod the followi
3. Kleinberg, Jon. Algorithm Design (p. 519, q. 28) Consider this version of the Independent Set Problem. You are given an undirected graph G and an integer k. We will call a set of nodes I "strongly independent" if, for any two nodes v, u € I, the edge (v, u) is not present in G, and neither is there a path of two edges from u to v. That is, there is no node w such that both (v, w) and (u, w) are present. The Strongly Independent Set problem is to decide whether G has a strongly independent set of size at least k. Show that the Strongly Independent Set Problem is NP-Complete.
1. Run DFS-with-timing on this graph G: give the pre and post number of each vertex. Whenever there is a choice of vertices to explore, always pick the one that is alphabetically first. 2. Draw the meta-graph of G. 3. What is the minimum number of edges you must add to G to make it strongly connected (i.e., it consists of a single connected component after adding these edges)? Give such a set of edges. b.

SEE MORE QUESTIONS

Recommended textbooks for you

Database System Concepts

Computer Science

ISBN:

9780078022159

Author:

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

Publisher:

McGraw-Hill Education

Starting Out with Python (4th Edition)

Computer Science

ISBN:

9780134444321

Author:

Tony Gaddis

Publisher:

PEARSON

Digital Fundamentals (11th Edition)

Computer Science

ISBN:

9780132737968

Author:

Thomas L. Floyd

Publisher:

PEARSON

Database System Concepts

Computer Science

ISBN:

9780078022159

Author:

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

Publisher:

McGraw-Hill Education

Starting Out with Python (4th Edition)

Computer Science

ISBN:

9780134444321

Author:

Tony Gaddis

Publisher:

PEARSON

Digital Fundamentals (11th Edition)

Computer Science

ISBN:

9780132737968

Author:

Thomas L. Floyd

Publisher:

PEARSON

C How to Program (8th Edition)

Computer Science

ISBN:

9780133976892

Author:

Paul J. Deitel, Harvey Deitel

Publisher:

PEARSON

Database Systems: Design, Implementation, & Manag…

Computer Science

ISBN:

9781337627900

Author:

Carlos Coronel, Steven Morris

Publisher:

Cengage Learning

Programmable Logic Controllers

Computer Science

ISBN:

9780073373843

Author:

Frank D. Petruzella

Publisher:

McGraw-Hill Education

SEE MORE TEXTBOOKS