Please solve and show all work. WFigure 20.6 A directed graph for use in Exercises 20.3-2 and 20.5-2.20.3-2Show how depth-first search works on the graph of Figure 20.6. Assume that the for loop oflines 5-7 of the DFS procedure considers the vertices in alphabetical order and assume thateach adjacency list is ordered alphabetically. Show the discovery and finish times for eachvertex, and show the classification of each edge.

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

Answered: W Figure 20.6 A directed graph for 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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Write to code describes how to create the links dataset that represents the input graph. In this particular case, the links represent a directed network. The links dataset has only the nodes identification, which means, the from and to variables. The link weights in the transitive closure problem are irrelevant. In other words, it doesn’t matter the cost or the weight of the links, the algorithm searches for the possible paths to connect the nodes within the input graph. If there is a link or a set of links, no matter the weights, that connects node i to node j, that is the matter.
Using the same graph as in the previous question, list the vertices in the order thatthey will be visited by a breadth-first traversal, starting withe vertex A. Again, when there are multiple adjacent vertexes, save them alphabetically, A to G.Enter the letters with no spaces between them, in the order they would be visited.
Given the following graph find all articulation points. If necessary, consider nodes and edges in alphabetical order. H. Display all articulation points alphabetically. Please, report only the list of vertices separated by a single space. No other symbols must be included in the response. This is an example of the response format: ABC etc. Computer Science Please not Calculus
Write algorithm LargestShortestWeight(G, s,t) pre-cond: G is a weighted directed (augmenting) graph. s is the sourcenode.t is the sink. post-cond: P specifies a path from s to t whose smallest edge weight is aslarge as possible. u, v is its smallest weighted edge.
How many entries would the adjacency list representation for the following graph contain? (Assume that the array slots for each vertex count as one entry, and the linked list nodes for edges each count as one entry as well.) D B E A F G
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.
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?
Implement a program that performs a depth-first search on the graph shown in Figure.
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
Consider the following graph: a Specify a simple cycle. Use only lower case letters. If the graph has any cycles which are not simple and which have no repeated edges, specify one. If there are none enter none Use only lower case letters.
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
If there is an Euler path that starts at AA and ends at some other vertex, give it. Otherwise enter DNE.This should be a list of letters, from A to the other vertex: e.g. ACBDEAD (if that were even possible!). Path: Since this is a planar graph, the number of regions - arcs + nodes equals what number?

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