1. Consider the following weighted graph. F B 10 5 G 15 E 30 D 5 10 5 15 20 A (a) Apply Dijkstra's Algorithm to the graph with A as the source/root and draw the graph for EACH step of the algorithm (include the initial state!). (b) Draw the minimum distance spanning tree associated with the algorithm with A as the root. Label the vertices! (c) Suppose a new graph is formed by deleting the edge between D and E. Run Dijkstra's Algorithm on this new graph with A as the source/root. You only need to provide the final graph produced by the algorithm.

1. Consider the following weighted graph. F B 10 5 G 15 E 30 D 5 10 5 15 20 A (a) Apply Dijkstra's Algorithm to the graph with A as the source/root and draw the graph for EACH step of the algorithm (include the initial state!). (b) Draw the minimum distance spanning tree associated with the algorithm with A as the root. Label the vertices! (c) Suppose a new graph is formed by deleting the edge between D and E. Run Dijkstra's Algorithm on this new graph with A as the source/root. You only need to provide the final graph produced by the algorithm.

Fundamentals of Information Systems

8th Edition

ISBN:9781305082168

Author:Ralph Stair, George Reynolds

Publisher:Ralph Stair, George Reynolds

Chapter3: Database Systems And Applications

Section: Chapter Questions

Problem 2.1DQ

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Give answer step by step diagram Find The Minimum Spanning Tree For the below undirected graph using prim's algorithm
Consider the undirected graph in Figure 1.a) Write down the adjacency matrix and adjacency lists specifying this graph. Assume that therows, columns and vertices in the adjacency list follow the alphabetical order of the vertex labels.b) Starting at vertex "S' and resolving ties by the vertex alphabetical order, traverse the graphby breadth first search and construct the corresponding breadth first search tree.
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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?
For each graph representation, select the appropriate worst-case time complexity for printing the vertex label of all the neighbors of a given vertex. Assume that vertex label retrieval from a typical integer vertex representation is O(1). Adjacency Matrix: ________ Edge List: ________ Adjacency List: _________ Choices: O(V+E), O(E^2), O(V^2), O(E)
Consider a weighted graph in which all the weights on the edges are distinct. Suppose that e is the edge with the largest weight. What is the property that the graph must have in order for e to be in the minimum spanning tree? Question options: 1) The graph must be a tree. 2) The edge e must be incident to a vertex of degree 1. 3) The weight of e must be close to the next largest weight. 4) The graph is no longer connected if e is removed.
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