A chicken farmer wishes to provide electric power to each chicken house on his farm by installing buried electrical power lines. The graph below illustrates the locations of the houses and the distances between them in feet. Use Kruskal's algorithm to determine how the farmer should dig channels in order to minimize the amount of digging. Also determine the minimum total length of channels that must be dug.
A chicken farmer wishes to provide electric power to each chicken house on his farm by installing buried electrical power lines. The graph below illustrates the locations of the houses and the distances between them in feet. Use Kruskal's algorithm to determine how the farmer should dig channels in order to minimize the amount of digging. Also determine the minimum total length of channels that must be dug.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A chicken farmer wishes to provide electric power to each chicken house on his farm by installing buried electrical power lines. The graph below illustrates the locations of the houses and the distances between them in feet. Use Kruskal's algorithm to determine how the farmer should dig channels in order to minimize the amount of digging. Also determine the minimum total length of channels that must be dug.
Transcribed Image Text:This image is a diagram depicting a network graph, where each circle represents a node and each line connecting the nodes is an edge. The numbers on the edges indicate the weights or values associated with those connections.
Nodes:
- The graph consists of six nodes.
Edges and Weights:
- There are multiple edges connecting the nodes with various weights.
- Example connections with weights include:
- Node 1 to Node 2: 88
- Node 1 to Node 3: 150
- Node 1 to Node 4: 137
- Node 1 to Node 5: 110
- Node 1 to Node 6: 55
- Node 2 to Node 3: 92
- Node 2 to Node 4: 149
- Node 2 to Node 5: 118
- Node 2 to Node 6: 46
- Node 3 to Node 4: 115
- Node 3 to Node 5: 123
- Node 3 to Node 6: 131
- Node 4 to Node 5: 128
- Node 4 to Node 6: 78
- Node 5 to Node 6: 105
The graph can be used to study various properties of networks, such as shortest paths between nodes, network flow, connectivity, or optimization problems. The weights might represent distances, costs, or other quantitative measures significant to the relationship between the nodes.
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