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Abstract

A graph on n vertices is said to admit a prime labeling if we can label its vertices with the first n natural numbers such that any two adjacent vertices have relatively prime labels. Here we extend the idea of prime labeling to the Gaussian integers, which are the complex numbers whose real and imaginary parts are both integers. We begin by defining an order on the Gaussian integers that lie in the first quadrant. Using this ordering, we show that all trees of order at most 72 admit a prime labeling with the Gaussian integers.

Author Bio

Hunter Lehmann (lehmannh@seattleu.edu) is a 2016 Seattle University graduate with a BS in Pure Mathematics. Besides math, he enjoys reading sci-fi and fantasy novels and soccer refereeing. He will be attending graduate school at the University of Kentucky in the fall and hopes to one day teach at the university level.

Andrew Park (parka@seattleu.edu) is a 2016 Seattle University graduate with a BS in Pure Mathematics and a minor in Electrical Engineering. He likes Super Smash Bros., Melee, and rock climbing. His plans for the future are to be employed and happy.

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