How How to Use Graph Theory Benefiting the Neighborhoods Environment

Abstract

Graph Theory is a popular field with wide applications. It also has the reputation of being the type of math that is more up-to-date with modern times. However, a quick search of the math curriculum at the secondary level will show a striking absence. This paper hopes to reverse the trend and bring to light both a way to introduce graph theory and also to show the application to the real world all in one unified story. Within this article, the reader will move from little to no knowledge toward a fundamental understanding of one component of graph theory. The reader will also be able to walk away with the ability to analyze efficient routes in real-world networks. This work is a crafted message, a student-to-student message, on building intuition for theories and then using them directly. This article is primarily an argument for the importance of engaging with graph theory early in mathematics study. It argues that graph theory is more than a fashionable buzzword. It is the methodical study of interconnection, and it applies to most of the biggest critical global problems we face today: Environmental Protection, Nuclear Safety, Global Food Supply, and Artificial Intelligence Control. In the end, this article may focus on building one application, resource conservation, and logistic optimization, though the reach will be much further. The tools of graph theory are easily adapted to any problem involving systems and their related parts.