Solve C, D, E pleaseThankYou. ## Directed Graph of Chicago's 'L' System### Description of the GraphThe 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\

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?