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$1$ $\underline{\text{Binomial Coefficient}}$ $\underline{\text{An Introduction to Graph Theory}}$  \vspace{2mm}  The concepts of graph theory go all the way back to the eighteenth century when, in 1736, Euler published what is believed to be the first paper on the very subject. It contained a famous problem known as the Konigsberg Bridges Problem. This is a puzzle which considers the question of whether or not a person, starting from their home, could pass over each of the seven bridges that crossed the Pregal River exactly once before returning home. Euler was able to reconstruct the problem in such a way that allowed for him to lay the foundation of graph theory. To solve the puzzle, Euler replaced the land masses with vertices and let edges represent the bridges. The mathematical structure that became of his work is now called a graph.