# Applications of Discrete Mathematics and Statistics in IT

*label*Computer Science

*timer*Asked: Oct 22nd, 2015

**Question description**

· The following graph represents a portion of the subway system of a city. The vertices on the graph correspond to subway stations, and the edges correspond to the rails. Your job is to write a program for a cleaning car to efficiently clean this portion of the subway system.

a. Using Euler’s theorem, explain why it is possible to pass through all of the stations by traversing every rail only once.

b. Using Fleury’s algorithm, provide an optimal path to clean all the rails by passing through them only once.

c. Is it possible to find an optimal path described in question 3-b that starts on any station? Explain your answer.

d. Is it possible to find an optimal path described in question 3-b that starts and ends at the same station? Explain why or why not.