Consider the graph given above. Use the sorted edges algorithm to find a Hamiltonian circuit. a. List the weights of the edges separated by commas in the Hamiltonian circuit in the order they are chosen as specified by the algorithm.
Consider the graph given above. Use the sorted edges algorithm to find a Hamiltonian circuit. a. List the weights of the edges separated by commas in the Hamiltonian circuit in the order they are chosen as specified by the algorithm.
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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Consider the graph given above. Use the sorted edges algorithm to find a Hamiltonian circuit.
a. List the weights of the edges separated by commas in the Hamiltonian circuit in the order they are chosen as specified by the algorithm.
Transcribed Image Text:The image depicts a graph configured as a hexagon with seven distinct vertices labeled as S, R, Q, V, U, T, and S. These vertices are connected by edges, each marked with numbers from 3 to 17. Here's a detailed explanation:
### Description of the Graph:
- **Vertices:**
- The hexagon comprises six outer vertices: S, R, Q, V, U, and T.
- Each vertex is marked by a blue dot.
- **Edges and Numbering:**
- The edges connect the vertices in various ways, forming both a surrounding hexagon and internal intersecting lines.
- The edges within the graph are labeled with red numbers:
- S to R: 7
- S to Q: 3
- S to T: 5
- S to V: 6
- S to U: 4
- R to Q: 6
- R to V: 12
- R to T: 8
- R to U: 7
- Q to V: 9
- Q to T: 12
- Q to U: 11
- T to U: 15
- T to V: 14
- U to V: 17
### Connectivity:
- The graph has a mix of outer and intersecting inner lines, signifying connected paths between vertices.
- The labeling indicates possibly weighted edges, useful for studying paths and connections within graph theory.
This graph is ideal for illustrating concepts such as networking, shortest path algorithms, and relationships among weights and paths in an educational setting.
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