Document Type

Honors

Department

Mathematical Sciences

Rights Management

Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International license (CC BY-NC-ND 4.0)

Abstract

Trains, a method of transportation for people and/or goods, are different than other methods of transportation, such as boats or trucks. Trains can only travel in a railroad system, specifically upon tracks. If something is prevent ing the train from moving on the tracks, then that whole line of railroad is shut down. If boats and trucks cannot travel on a particular route, there are alternative routes that can be taken. The design of the railroad system may appear to be created by chance, in that no trains crash into each other or into stations, but there is an application to graph theory which can help determine safety and efficiency in the railroad system. Additionally, there are types of graphs and information that are used specifically for railroad systems in graph theory, which will be discussed briefly. In this paper, there is an introduction to graph theory, its properties, and a basic application of graph theory to the railroad system. Additionally, three train lines in the London Underground are transformed into graphs, each of which are then analyzed, in respect to one of three design and safety problems of railroad systems (the blocking problem, the yard location problem, and the train schedule problem). Overall, it was found that graph theory is effective in developing railroad systems and that the three design and safety problems of railroad systems can be analyzed by using graph theory.

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