Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
a 14 D 15 10- B Apply the sorted edges algorithm to the graph above. Find the total cost of the resulting circuit.

a 14 D 15 10- B Apply the sorted edges algorithm to the graph above. Find the total cost of the resulting circuit.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.3: Systems Of Inequalities
Problem 15E
See similar textbooks
icon
Related questions
Question
### Applying the Sorted Edges Algorithm #### Graph Explanation The image shows a weighted graph with four vertices labeled \(A\), \(B\), \(C\), and \(D\). The edges connecting these vertices have the following weights: - Edge \(A - C\): 1 - Edge \(A - D\): 5 - Edge \(A - B\): 10 - Edge \(C - D\): 14 - Edge \(C - B\): 6 - Edge \(D - B\): 15 #### Problem Statement **Task**: Apply the sorted edges algorithm to the graph above. Find the total cost of the resulting circuit. ### Steps Using the Sorted Edges Algorithm 1. **List the Edges in Order of Increasing Weight**: - \(A - C\): 1 - \(A - D\): 5 - \(C - B\): 6 - \(A - B\): 10 - \(C - D\): 14 - \(D - B\): 15 2. **Select Edges to Form a Circuit**: The sorted edges algorithm involves selecting edges in order of increasing weight, ensuring that no cycles are formed until all vertices are connected. - Select edge \(A - C\) (Weight 1) - Select edge \(A - D\) (Weight 5) - Select edge \(C - B\) (Weight 6) At this point, we have connected all vertices: \(A\), \(B\), \(C\), \(D\). Note that selecting the edge \(A - B\) would form a cycle. #### Total Cost Calculation The selected edges are: - \(A - C\) (Weight 1) - \(A - D\) (Weight 5) - \(C - B\) (Weight 6) **Total Cost** = 1 + 5 + 6 = 12 Therefore, the total cost of the resulting circuit is **12**.
Transcribed Image Text:### Applying the Sorted Edges Algorithm #### Graph Explanation The image shows a weighted graph with four vertices labeled \(A\), \(B\), \(C\), and \(D\). The edges connecting these vertices have the following weights: - Edge \(A - C\): 1 - Edge \(A - D\): 5 - Edge \(A - B\): 10 - Edge \(C - D\): 14 - Edge \(C - B\): 6 - Edge \(D - B\): 15 #### Problem Statement **Task**: Apply the sorted edges algorithm to the graph above. Find the total cost of the resulting circuit. ### Steps Using the Sorted Edges Algorithm 1. **List the Edges in Order of Increasing Weight**: - \(A - C\): 1 - \(A - D\): 5 - \(C - B\): 6 - \(A - B\): 10 - \(C - D\): 14 - \(D - B\): 15 2. **Select Edges to Form a Circuit**: The sorted edges algorithm involves selecting edges in order of increasing weight, ensuring that no cycles are formed until all vertices are connected. - Select edge \(A - C\) (Weight 1) - Select edge \(A - D\) (Weight 5) - Select edge \(C - B\) (Weight 6) At this point, we have connected all vertices: \(A\), \(B\), \(C\), \(D\). Note that selecting the edge \(A - B\) would form a cycle. #### Total Cost Calculation The selected edges are: - \(A - C\) (Weight 1) - \(A - D\) (Weight 5) - \(C - B\) (Weight 6) **Total Cost** = 1 + 5 + 6 = 12 Therefore, the total cost of the resulting circuit is **12**.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Elementary Algebra
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
SEE MORE TEXTBOOKS