7. Use Prim's algorithm to find the minimum weighted spanning tree for the graph infigure K₂.a7b155j63 510K,a. How many vertices are there?d.80h12b. How many edges will be in the spanning tree?c. What is the minimum edge that we can start with? d. Complete the table below for iterations 1-7.Iterations What are edges in this iteration?1-71234567Note: We can't use {c, d) because that will create acircuit.e. What is the sum of all the edges?What is the minimum edgefrom this iteration?Use the minimum edge (b, c)

Answered: 7. Use Prim's algorithm to find the…

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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7. Use Prim's algorithm to find the minimum weighted spanning tree for the graph in
figure K₂.
a
7
b
15
5
j
6
3 5
10
K,
a. How many vertices are there?
d.
80
h
12
b. How many edges will be in the spanning tree?
c. What is the minimum edge that we can start with?

d. Complete the table below for iterations 1-7.
Iterations What are edges in this iteration?
1-7
1
2
3
4
5
6
7
Note: We can't use {c, d) because that will create a
circuit.
e. What is the sum of all the edges?
What is the minimum edge
from this iteration?
Use the minimum edge (b, c)

Expert Solution

Step 1

Prim's algorithm:

Prim's algorithm is a greedy algorithm used to find the minimum spanning tree of a graph. It works by starting from a single node and exploring its neighboring nodes, finding the lowest cost edge from the source node to any of its neighboring nodes. This edge is then added to the minimum spanning tree, and the algorithm then continues to explore the neighboring nodes of the newly added edge, until all nodes are part of the minimum spanning tree. This algorithm is useful for finding the least expensive path to connect all nodes in a graph.

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