. B-Tree of order 4 • Each node has at most 4 pointers and 3 keys, and at least 2 pointers and 1 key. • Insert: 5, 3, 21, 9, 1, 13, 2. 7. 10. 12, 4, 8 . Graphs A 5 . 10 . 15 C 10 B 10 D 3 30 20 E 1. Construct the following Graph Representation from given Directed Graph above. Adjacency Matrix Adjacency List 15 FL

. B-Tree of order 4 • Each node has at most 4 pointers and 3 keys, and at least 2 pointers and 1 key. • Insert: 5, 3, 21, 9, 1, 13, 2. 7. 10. 12, 4, 8 . Graphs A 5 . 10 . 15 C 10 B 10 D 3 30 20 E 1. Construct the following Graph Representation from given Directed Graph above. Adjacency Matrix Adjacency List 15 FL

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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Draw a tree with 14 vertices Draw a directed acyclic graph with 6 vertices and 14 edges Suppose that your computer only has enough memory to store 40000 entries. Which best graph data structure(s) – you can choose more than 1 -- should you use to store a simple undirected graph with 200 vertices, 19900 edges, and the existence of edge(u,v) is frequently asked? - Adjacency Matrix - Adjacency List - Edge List
Kruskal's minimum spanning tree algorithm is executed on the following graph. Select all edges from edgeList that belong to the minimum spanning tree. edgeList result List AD BC BE CF EF DG EG EH GH D 7 9 G 1 B 5 3 A E H 4 2 6 8 F
6 591 9 1 75 1 3 10 8 8 5 8 G746
4. Please apply Kruskal's spanning tree algorithm in the graph below and find the minimum spanning tree (MST). Edge weights are in the adjacency matrix table. (you can list the edges in MST or draw the tree below) d b a e h f The adjacency matrix for the undirected weighted graph is mentioned below: a d e g h a 4 8 4 8 11 8. 7 4 2 d 7 14 e 9. 10 f 4 14 10 2 1 6. 8. 11 1 7 7
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.
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;
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?
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
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
Question 16 Find the list of vertices following the breadth-first traversal of the graph below starting from vertex A. ( Note: when two or more nodes are equally as likely to be selected, select the one that comes fırst alphabetically). Enter your answer as a list of nodes with no space (or any other separator) between them. J D (A E
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.
3. From the graph above determine the vertex sequence of the shortest path connecting the following pairs of vertex and give each length: a. V & W b. U & Y c. U & X d. S & V e. S & Z 4. For each pair of vertex in no. 3 give the vertex sequence of the longest path connecting them that repeat no edges. Is there a longest path connecting them?