Figure 16: An undirected weighted graph has 6 vertices, a through f, and 9 edges. Verter d is on the left. Verter f is above and to the right of verter d. Verter e is below and to the right of verter f, but above verter d. Verter c is below and to the right of verter e. Verter a is above verter e and to the right of verter c. Verter b is below and to the right of verter a, but above verter c. The edges between the vertices and their weight are as follows: d and f, 1; d and e, 4; ƒ and e, 2; e and a, 2; f and a, 3; e and e, 5; c and a, 7; e and b, 5; and a and b, 6. (a) Use Prim's algorithm to compute the minimum spanning tree for the weighted graph. Start the algorithm at vertex a. Show the order in which the edges are added to the tree.

Figure 16: An undirected weighted graph has 6 vertices, a through f, and 9 edges. Verter d is on the left. Verter f is above and to the right of verter d. Verter e is below and to the right of verter f, but above verter d. Verter c is below and to the right of verter e. Verter a is above verter e and to the right of verter c. Verter b is below and to the right of verter a, but above verter c. The edges between the vertices and their weight are as follows: d and f, 1; d and e, 4; ƒ and e, 2; e and a, 2; f and a, 3; e and e, 5; c and a, 7; e and b, 5; and a and b, 6. (a) Use Prim's algorithm to compute the minimum spanning tree for the weighted graph. Start the algorithm at vertex a. Show the order in which the edges are added to the tree.

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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5. Vertices: (a, b, c, d, e, f, g) Edges: {(a, b), (a, f), (b, e), (b, g). (c. f). (c. g). (c. d), (d. e), (d. g} } Draw a Graph for the given vertices and edges. Find the adjacent vertices of a vertex c. Find the shortest path between source vertex f and destination vertex e.
An undirected weighted graph G is given below Figure 16: An undirected weighted graph has 6 vertices, a through f, and 9 edges. Vertex d is on the left. Vertex f is above and to the right of vertex d. Vertex e is below and to the right of vertex f, but above vertex d. Vertex c is below and to the right of vertex e. Vertex a is above vertex e and to the right of vertex c. Vertex b is below and to the right of vertex a, but above vertex c. The edges between the vertices and their weight are as follows: d and f, 1; d and e, 4; f and e, 2; e and a, 2; f and a, 3; e and c, 5; c and a, 7; c and b, 5; and a and b, 6. (a) What is the minimum weight spanning tree for the weighted graph subject to the condition that edge {d, e} is in the spanning tree? (b) How would you generalize this idea? Suppose you are given a graph G and a particular edge {u, v} in the graph. How would you alter Prim’s algorithm to find the minimum spanning tree subject to the condition that {u, v} is in the tree?
3. Draw a connected graph with 4 vertices, each of degree 3.
2. Use the following description of an undirected graph and draw the graph: v(Graph1) = { A, B, C, D} E(Graph1) = { (A,B), (A,D), (B,C), (B,D) }
An undirected weighted graph G is given below: Figure 16: An undirected weighted graph has 6 vertices, a through f, and 9 edges. Vertex d is on the left. Vertex f is above and to the right of vertex d. Vertex e is below and to the right of vertex f, but above vertex d. Vertex c is below and to the right of vertex e. Vertex a is above vertex e and to the right of vertex c. Vertex b is below and to the right of vertex a, but above vertex c. The edges between the vertices and their weight are as follows: d and f, 1; d and e, 4; f and e, 2; e and a, 2; f and a, 3; e and c, 5; c and a, 7; c and b, 5; and a and b, 6.(a) Use Prim’s algorithm to compute the minimum spanning tree for the weighted graph. Start the algorithm at vertex a. Show the order in which the edges are added to the tree.(b) What is the minimum weight spanning tree for the weighted graph in the previous question subject to the condition that edge {d, e} is in the spanning tree?(c) How would you generalize this idea? Suppose…
Vertices should be named by the letters in the alphabeth : A, B, C, D, EEdges should be named : e1,e2, e3, e4, e5, e6, e7, e8, e9 Draw or Make a Directed graph with 9 edges and 5 vertices
An undirected weighted graph G is given below: 3 .2 5 Figure 16: An undirected weighted graph has 6 vertices, a through f, and 9 edges. Verter d is on the left. Verter f is above and to the right of verter d. Verter e is below and to the right of verter f, but above vertez d. Verter e is belou and to the right of vertez e. Vertez a is above verter e and to the right of verter c. Verter 6 is below and to the right of vertez a, but above vertez e. The edges between the vertices and their weight are as follous: d and f, 1; d and e, 4: f and e, 2; e and a, 2: f and a, 3; e and c, 5; e and a, 7; e and b, 5; and a and b, 6. Use Prim's algorithm to compute the minimum spanning tree for the weighted graph. Start the algorithm at vertex a. Show the order in which the edges are added to the tree. What is the minimum weight spanning tree for the weighted graph in the previous question subject to the condition that edge {d, e} is in the span- ning tree? How would you generalize this idea? Suppose…
35. Any simple graph with n vertices is connected if it has A. Less than (n)(n-1)/3 edges B. Less than (n-1)(n-2)/2 edges C. More than n(n-1)/2 edges D. None of the above
37. A graph is connected if and only if there is a A. Path B. Trail C. Walk D. All of the Above between each pair of vertices.
1. Draw an undirected graph using the following set of edges. A={{1,4},{4,6},{6,5},{5,2},{2,1},{3,1},{2,3},{3,5},{6,3},{3,4}} a. What is the degree of each of the nodes in this graph? b. Is this graph regular?
(a) Create a graph with six vertices of degrees 2, 2, 2, 3, 4 and 5. Construct the matrixof the graph you created. Show your results clearly.(b) Create a graph with six vertices of degrees 0, 2, 3, 4, 5, and 6. Construct the matrixof the graph you created. Show your results clearly.(c) Create a graph with six vertices of degrees 0, 1, 2, 3, 4, and 5. Construct the matrixof the graph you created. Show your results clearly.
Suppose a graph has five vertices of degree 2 and three vertices of degree 3 and the remaining vertices are of degree 1. If the graph has 16 edges, what is the number of vertices of degree 1. Please do not use drawing for your answer.