Infinitely-many Primes in \(\mathbb{N}\): A Graph Theoretic Approach

A graph \(G\) is defined encapsulating the number theoretic notion of the Fundamental Theorem of Arithmetic. We then provide a graph theoretic approach to the fundamental results on the coprimality of two natural numbers, through the use of an adjacency operator \(\hat{\mathbf{A}}(G)\). Lastly, these results are used to give an alternate proof to the known result that there are infinitely many primes in the natural numbers \(\mathbb{N}\).