Graphs and Their Algorithms
by Robert Emord
Two Semester Project
Advised by Prof. Armen
With Mathematical help from Prof. Georges

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“12:45 restate my assumptions. One, math is the language of nature. Two, everything around us can be represented and understood through numbers. Three, if you graph the numbers in any system patterns emerge, therefore there are patterns everywhere in nature”(Watson). Obviously, this is not a proven fact merely a conjecture, but the meaning is sufficient. Mathematics is everywhere in nature and science. In most cases, nature can be represented in a graph. A graph, denoted G = (V, E), is a set of finite vertices V, the set of finite edges E, and their relationship. Many complex problems can be easily solved once modeled into a graph. For instance, there is the well-known traveling salesman problem that can be solved using a complex linear algebra equation or a graph theory algorithm for one to find the shortest and most efficient route to reach all of his/her destinations. Graphs also play a large role in networks. When a computer searches for a web page or receives packets from the Internet graph theory algorithms are used to find the proper route.



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