### Graph DescriptionThe graph consists of 8 vertices labeled \( A, B, C, D, E, F, G, \) and \( H \). The edges connecting these vertices have the following weights:- \( A \) to \( B \): 5- \( A \) to \( H \): 10- \( A \) to \( G \): 20- \( A \) to \( D \): 5- \( B \) to \( C \): 5- \( B \) to \( D \): 50- \( C \) to \( D \): 20- \( D \) to \( E \): 15- \( E \) to \( F \): 15- \( F \) to \( G \): 25- \( F \) to \( D \): 30- \( G \) to \( H \): 10- \( H \) to \( G \): 10- \( H \) to \( F \): 5### Questions1. Use the graph to answer the following questions: (a) **Kruskal’s Algorithm**: Produce a minimum spanning tree by writing down the edges you choose in the order of the algorithm. (b) **Prim’s Algorithm**: Produce a minimum spanning tree assuming vertex \( A \) is the root/source. Write down the edges you choose in the order of the algorithm.

Answer : Using kruskal's algorithom : The graph contains 8 vertices and 13 edges. So, the minimum…

1. Use the graph below to answer the following questions. A 5 B H 10 G 10 25 20 50 5 5 30 15 5 E 15 C 20 F (a) Use Kruskal's Algorithm to produce a minimum spanning tree. Write down the edges that you choose in order of the algorithm. D

1. Use the graph below to answer the following questions. A 5 B H 10 G 10 25 20 50 5 5 30 15 5 E 15 C 20 F (a) Use Kruskal's Algorithm to produce a minimum spanning tree. Write down the edges that you choose in order of the algorithm. D

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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Concept explainers

Minimum Spanning Tree

A spanning tree is a sub-graph of a connected, undirected graph. It has all the vertices of a graph with the minimum possible number of edges. If a vertex is skipped, then it will not be a spanning tree. The edges of a spanning tree may or may not have weights.

Question

### Graph Description

The graph consists of 8 vertices labeled \( A, B, C, D, E, F, G, \) and \( H \). The edges connecting these vertices have the following weights:

- \( A \) to \( B \): 5
- \( A \) to \( H \): 10
- \( A \) to \( G \): 20
- \( A \) to \( D \): 5
- \( B \) to \( C \): 5
- \( B \) to \( D \): 50
- \( C \) to \( D \): 20
- \( D \) to \( E \): 15
- \( E \) to \( F \): 15
- \( F \) to \( G \): 25
- \( F \) to \( D \): 30
- \( G \) to \( H \): 10
- \( H \) to \( G \): 10
- \( H \) to \( F \): 5

### Questions

1. Use the graph to answer the following questions:

(a) **Kruskal’s Algorithm**:
Produce a minimum spanning tree by writing down the edges you choose in the order of the algorithm.

(b) **Prim’s Algorithm**:
Produce a minimum spanning tree assuming vertex \( A \) is the root/source. Write down the edges you choose in the order of the algorithm.

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