Consider the following directed graph G as shown in Figure 2. Answer the following. a) Is the graph strongly connected? Justify your answer. b) Apply Depth-First Search (DFS) algorithm over this graph and find each vertex's discovery and finishing time. Explore/visit the nodes in alphabetic order in cases where you have multiple options. c) Mark all the edges of this graph accordingly. d) How many strongly connected component the graph has? Justify your answer. B A D F E H

Consider the following directed graph G as shown in Figure 2. Answer the following. a) Is the graph strongly connected? Justify your answer. b) Apply Depth-First Search (DFS) algorithm over this graph and find each vertex's discovery and finishing time. Explore/visit the nodes in alphabetic order in cases where you have multiple options. c) Mark all the edges of this graph accordingly. d) How many strongly connected component the graph has? Justify your answer. B A D F E H

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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Assume you are to write a program to analyze the social connection between students in MTSU. Each student is a node in a undirected graph. An edge is added between two nodes if these two students have close social connections, i.e., in the same club, or in the same department. Which would be a better representation for this graph? Question 45 options: adjacency matrix representation adjacency list representation
Consider the graph depicted below. Answer the following questions: What is the degree of vertex a? What is the sum of degrees of all vertices? Who are the neighbors of vertex f? [Please, give the list in alphabetical order, separating letters with only a comma. Do not insert blank spaces] How many zeros does the adjacency matrix of the graph above contain? What is the value on row g and column d of the adjacency matrix?
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.
Can you help me with this problem and can you do it step by step. question: Show that every graph with two or more nodes contains two nodes that have equal degrees.
Create a weighted connected graph with the following characteristics: The assigned number of vertices are alphabetically labeled starting with A. Vertex Ais not adjacent to vertex G. At leasttwovertices have a degree greater than 2. Allweights are greater than 0. • No weights are the same.
Create a weighted connected graph with the following characteristics: 11 vertices are alphabetically labeled starting with A. Vertex A is not adjacent to vertex G. At least two vertices have a degree greater than 2. All weights are greater than 0. No weights are the same.
8. Consider the following directed graph G as shown in Figure 2. Answer the following. a) Is the graph strongly connected? Justify your answer. b) Apply Depth-First Search (DFS) algorithm over this graph and find each vertex's discovery and finishing time. Explore/visit the nodes in alphabetic order. c) Mark all the edges of this graph accordingly. d) How many strongly connected component the graph has? Justify your answer. A E B F H G
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
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.
You are given a connected, undirected graph G. Devise an algorithm that produces a path that traverses each edge in G exactly once in each direction. A vertex may occur multiple times on the path. Provide a short justification about why your algorithm is correct, and analyze its efficiency.
Given N cities represented as vertices V₁, V2, un on an undirected graph (i.e., each edge can be traversed in both directions). The graph is fully-connected where the edge eij connecting any two vertices vį and vj is the straight-line distance between these two cities. We want to search for the shortest path from v₁ (the source) to VN (the destination). ... Assume that all edges have different values, and €₁,7 has the largest value among the edges. That is, the source and destination have the largest straight-line distance. Compare the lists of explored vertices when we run the uniform-cost search and the A* search for this problem. Hint: The straight-line distance is the shortest path between any two cities. If you do not know how to start, try to run the algorithms by hand on some small cases first; but remember to make sure your graphs satisfy the conditions in the question.
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