Consider the following graph: ![0 (graph_1.-png) 1. Write down the adjacency matrix and adjacency lists specifying this graph. (Assume that the matrix rows and columns and vertices in the adjacency lists follow in the alphabetical order of the vertex labels.) 2. Starting at vertex `a' order, traverse the graph by depth-first search and construct the corresponding depth-first search tree. Give the order in which the vertices were reached for the first time (pushed onto the traversal stack) and the order in which the vertices became dead ends (popped off the stack). and resolving ties by the vertex alphabetical

Consider the following graph: ![0 (graph_1.-png) 1. Write down the adjacency matrix and adjacency lists specifying this graph. (Assume that the matrix rows and columns and vertices in the adjacency lists follow in the alphabetical order of the vertex labels.) 2. Starting at vertex `a' order, traverse the graph by depth-first search and construct the corresponding depth-first search tree. Give the order in which the vertices were reached for the first time (pushed onto the traversal stack) and the order in which the vertices became dead ends (popped off the stack). and resolving ties by the vertex alphabetical

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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2. Consider the graph given by the following adjacency list: vertex adjacent vertics 1 2, 3, 4 2 1 3 1, 4 4 1, 3 5 - (a) Draw the corresponding graph. (b) Write down the adjacency matrix A for this graph. Calculate A2. What is the meaning of the entries of matrices A and A2? (c) Starting at vertex 4, use the adjacency matrix algorithm to check for connectivity. Please no plagiarism and also i want clear hand writting. Thanks
Given the following graph: 15 5. 13 4 a 11 e 12, 3 10 f 1 Type the weight of each edge in the order in which they will be selected when using Kruskal's algorithm to create a minimum spanning tree. Be sure to separate the weights using a single space. Do not separate them with commas or any other characters.
For the following graph, list the vertices in the order they might be encountered in a depth first search (DFS) starting at vertex A. No need to use any spaces, e.g., ACFGHIDBE In cases when there are multiple possibilities for the next vertex, choose them in alphabetical order (for reference: A, B, C, D, E, F, G, H, I) A B E
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…
2. Consider the graph G2(V2, E2) below. 2a. Find the MST of this graph with Kruskal’s algorithm. Draw the MST, and show the table [edge] [w(u, v)] [mark]. 2b. Find the MST of this graph with Prim’s algorithm starting at vertex 'a'. Draw the MST and list the vertices in order you added them to the MST. 2c. Would you get a different MST if you repeat 2b starting at vertex 'e'? Why or why not?
Weighted Graph Applications Demonstration Java Data Structures. Figure 29.23 illustrates a weighted graph with 6 vertices and 8 weighted edges. Simply provide: Minimal Spanning Tree as an illustration or a textual list of edges (in our standard vertex order). Single-Source Shortest Path route from vertex 0 to the other 5 (described as one path/route for each). draw the two solutions and attach the illustration or describe them in text (a list of edges for the one and the vertex to vertex path the other). You can therefore attach proper content files with dot txt, png, jpg or jpeg extensions Be sure the final trees or path lists are clearly visible in your solution. You don't need to show the solution development or progress, just the result.
Consider the following graph. Start from vertex x, use the Depth First Search (DFS) algorithm (described in the textbook) to compute the DFS tree(s). Show intermediate results similar to the textbook example and show the final DFS tree(s). It is assumed that in the adjacency list representation, all vertices are stored according to their alphabetical order. In other words, a vertex’s neighbors should be explored by their relative alphabetical order.
4. Consider the graph G, shown below, which is simply a copy of K5. 02 V3 5 V1 24 V5 How many distinct spanning trees does G have? (Hint: Break up your search by the isomorphism type of the tree, as discovered on the previous page. So for example, start by counting the paths of length 5 in G. Then proceed to the next type of tree with 5 vertices. The total number of trees is 125, but please use this answer only to check that your solution is complete!)
17 B 5 3 7 6 18 14 15 12 2 8 10 1 16 11 13 J 9 I 15 H a. Consider the graph given above. Use Prim's and Kruskal's algorithm to find the minimum spanning tree. b. What is the total weight of the spanning trees? List the weights of the selected edges separated by commas in the order of selection.
The Floyd-Warshall algorithm is a dynamic algorithm for searching the shortest path in a graph. Each vertex pair has its assigned weight. You are asked to draw the initial directed graph and show the tables for each vertex from Mo to Ms by finding all the shortest paths. Below is the algorithm as a guide. Algorithm 1: Pseudocode of Floyd-Warshall Algorithm Data: A directed weighted graph G(V, E) Result: Shortest path between each pair of vertices in G for each de V do | distance|d][d] «= 0; end for each edge (s, p) € E do | distance[s][p] + weight(s, p); end n = cardinality(V); for k = 1 to n do for i = 1 to n do for j = 1 to n do if distancefi][j] > distance/i][k] + distance/k][j] then | distance i]lj] + distancefi|[k] + distance/k|[j]; end end end end Consider the relation R = {(1,4) =4, (2,1)=3, (2,5)=-3, (3,4)=2, (4,2)=1, (4,3)=1, (5,4)=2 } on A = (1,2,3,4,5) solve the Floyd-Warshall Algorithm.
Give an example of a graph that has all 3 of the following properties. (Note that you need to give a single graph as the answer.) (i) It is connected (ii) It has one articulation point. (iii) The graph needs at least 4 colors for a valid vertex coloring (iv) The graph does not have a 4-clique (that is, a clique of 4 vertices) as a subgraph.
(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.