Given the following directed graph G representing Chicago's 'L' system: Morchandise Mart StatelLake Clark Lake WashingtonWells Washington/Wabash Washington Monroe Quincy Jackson Adama/Wabash Lasalle Van Buren Harold Washington Library UIC-Halsted Clinton LaSalle Answer the following questions and justify all your answers: a. Is there a walk of length greater than 5 from UIC-Halsted to Washington? b. Is there a path of length greater than 6 from UIC-Halsted to Clark/Lake? c. Is there a circuit of length greater than 9 starting at Clark/Lake? d. Is there a cycle of length greater than 2 starting at UIC-Halsted? e. Is there an edge from UIC-Halsted to Washington in G* for some even integer k?
Given the following directed graph G representing Chicago's 'L' system: Morchandise Mart StatelLake Clark Lake WashingtonWells Washington/Wabash Washington Monroe Quincy Jackson Adama/Wabash Lasalle Van Buren Harold Washington Library UIC-Halsted Clinton LaSalle Answer the following questions and justify all your answers: a. Is there a walk of length greater than 5 from UIC-Halsted to Washington? b. Is there a path of length greater than 6 from UIC-Halsted to Clark/Lake? c. Is there a circuit of length greater than 9 starting at Clark/Lake? d. Is there a cycle of length greater than 2 starting at UIC-Halsted? e. Is there an edge from UIC-Halsted to Washington in G* for some even integer k?
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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Solve C, D, E please
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Transcribed Image Text:## Directed Graph of Chicago's 'L' System
### Description of the Graph
The graph shown is a directed graph representing a portion of Chicago's 'L' system, with stations as nodes and connections as directed edges.
### Stations and Connections
- **UIC-Halsted** connects to **Clinton**.
- **Clinton** connects to **LaSalle** and **UIC-Halsted**.
- **LaSalle** connects to **LaSalle/Van Buren** and **Harold Washington Library**.
- **Harold Washington Library** connects to **Jackson**.
- **Jackson** connects to **Monroe** and **Adams/Wabash**.
- **Adams/Wabash** connects to **Washington/Wabash**.
- **Washington/Wabash** connects to **State/Lake**.
- **State/Lake** connects to **Washington**.
- **Washington** connects to **Clark/Lake**.
- **Clark/Lake** loops back to **Merchandise Mart** and **Washington/Wells**.
- **Merchandise Mart** connects back to **Clark/Lake** and down to **Washington/Wells**.
- **Washington/Wells** connects to **Clark/Lake** and **Quincy**.
- **Quincy** connects to **LaSalle/Van Buren**.
- **LaSalle/Van Buren** loops back to **LaSalle**.
### Questions
**a. Is there a walk of length greater than 5 from UIC-Halsted to Washington?**
- A walk is any sequence of nodes and directed edges. Check for sequences greater than 5 edges.
**b. Is there a path of length greater than 6 from UIC-Halsted to Clark/Lake?**
- A path does not repeat nodes. Look for distinct nodes with more than 6 connections.
**c. Is there a circuit of length greater than 9 starting at Clark/Lake?**
- A circuit starts and ends at the same node without repeating any edges. Explore routes originating from Clark/Lake.
**d. Is there a cycle of length greater than 2 starting at UIC-Halsted?**
- A cycle starts and ends at the same node without repeating nodes. Investigate cycles beginning from UIC-Halsted with more than 2 edges.
**e. Is there an edge from UIC-Halsted to Washington in \(G^k\
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