Abstract
Graph Theory is the study of mathematical graphs used to model the relationships between a network of vertices and edges. After Euler published his work on the Konigsberg Bridge Problem, the basic concepts behind his work expanded and graph theory is used in modern mathematical research, chemical and biological science and computer engineering. This project provides a simple demonstration of the uses of modern graph theory by formulating a “plan of travel” between five major international cities: Los Angeles, New York City, London, Paris and Tokyo. The process was twofold: to find a route with the lowest cost and a route with the shortest distance. The procedure included the utilization of the four major algorithms in graph theory (Nearest Neighbor, Sorted Edges, Brute Force Method, and Kruskal’s method) to create a “plan of travel” that would model the more sophisticated technology used by computer systems like MapQuest. This project concluded by finding the route with the lowest cost (LA-Tokyo-Paris-London-NYC-LA) and the route with the smallest distance (LA-Tokyo-Paris-London-NYC-LA
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