The graph below is used for problems 10, 11 and 12. A 31 В 40 20 22 21 35 26 33 -23 D 25 28 38 37 42. E 34 F 10. A mathematician applies the Greedy Algorithm to find the weight of the Hamiltonian circuit formed starting at vertex A. The order of the edges picked so far is AC, AF, BD, and CD. The next edge selected when applying the Greedy Algorithm should be a) DE b) BF c) EF d) none of these 11. The total weight of the circuit ABDFEA is a) 162 b) 147 c) 172 d) none of these 12. Using the Greedy Algorithm to find an approximate solution to the traveling salesman problem for a circuit starting at vertex D, the first edge to be selected should be а) BD b) AC c) AD d) none of these

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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**Transcription and Explanation for Educational Use**

**Graph Description:**

The graph in the image depicts a weighted complete graph with six vertices labeled A, B, C, D, E, and F. The edges connecting these vertices have weights assigned to them, representing distances or costs. Here are the weights for each edge:

- AB: 31
- AC: 20
- AD: 22
- AE: 23
- AF: 38
- BC: 21
- BD: 35
- BE: 40
- BF: 34
- CD: 33
- CE: 28
- CF: 42
- DE: 25
- DF: 37
- EF: 26

**Problems and Questions:**

**Problem 10:**
A mathematician applies the Greedy Algorithm to find the weight of the Hamiltonian circuit formed starting at vertex A. The order of the edges picked so far is AC, AF, BD, and CD. The next edge selected when applying the Greedy Algorithm should be:
- a) DE
- b) BF
- c) EF
- d) none of these

**Problem 11:**
The total weight of the circuit ABDFEA is:
- a) 162
- b) 147
- c) 172
- d) none of these

**Problem 12:**
Using the Greedy Algorithm to find an approximate solution to the traveling salesman problem for a circuit starting at vertex D, the first edge to be selected should be:
- a) BD
- b) AC
- c) AD
- d) none of these

The problems focus on applying the Greedy Algorithm to optimally select edges in a weighted graph, highlighting concepts related to Hamiltonian circuits and the Traveling Salesman Problem.
Transcribed Image Text:**Transcription and Explanation for Educational Use** **Graph Description:** The graph in the image depicts a weighted complete graph with six vertices labeled A, B, C, D, E, and F. The edges connecting these vertices have weights assigned to them, representing distances or costs. Here are the weights for each edge: - AB: 31 - AC: 20 - AD: 22 - AE: 23 - AF: 38 - BC: 21 - BD: 35 - BE: 40 - BF: 34 - CD: 33 - CE: 28 - CF: 42 - DE: 25 - DF: 37 - EF: 26 **Problems and Questions:** **Problem 10:** A mathematician applies the Greedy Algorithm to find the weight of the Hamiltonian circuit formed starting at vertex A. The order of the edges picked so far is AC, AF, BD, and CD. The next edge selected when applying the Greedy Algorithm should be: - a) DE - b) BF - c) EF - d) none of these **Problem 11:** The total weight of the circuit ABDFEA is: - a) 162 - b) 147 - c) 172 - d) none of these **Problem 12:** Using the Greedy Algorithm to find an approximate solution to the traveling salesman problem for a circuit starting at vertex D, the first edge to be selected should be: - a) BD - b) AC - c) AD - d) none of these The problems focus on applying the Greedy Algorithm to optimally select edges in a weighted graph, highlighting concepts related to Hamiltonian circuits and the Traveling Salesman Problem.
**13. The following graph has:**

![Graph with vertices A, B, C forming a triangle with an extra edge BC.]

a) an Eulerian circuit  
b) an Eulerian path but no Eulerian circuit  
c) neither an Eulerian circuit nor an Eulerian path.

**14. What is the smallest number of edges that must be added to eulerize the given graph?**

![Graph with two sets of intersecting triangles, forming a diamond shape.]

a) 0  
b) 1  
c) 2  
d) 3

**15. Which of the following paths is an Eulerian circuit for the given graph?**

![Graph with vertices labeled A to G, forming multiple intersecting triangles.]

a) ABEGFDACFDA  
b) ADFACFGEBA  
c) AFGEBACFA  
d) none of these
Transcribed Image Text:**13. The following graph has:** ![Graph with vertices A, B, C forming a triangle with an extra edge BC.] a) an Eulerian circuit b) an Eulerian path but no Eulerian circuit c) neither an Eulerian circuit nor an Eulerian path. **14. What is the smallest number of edges that must be added to eulerize the given graph?** ![Graph with two sets of intersecting triangles, forming a diamond shape.] a) 0 b) 1 c) 2 d) 3 **15. Which of the following paths is an Eulerian circuit for the given graph?** ![Graph with vertices labeled A to G, forming multiple intersecting triangles.] a) ABEGFDACFDA b) ADFACFGEBA c) AFGEBACFA d) none of these
Expert Solution
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The greedy algorithm is used to obtain an optimal Hamiltonian circuit for a graph. The selection of an edge in the greedy algorithm is done as per the weight of the edge.

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