(2,3)-Cordial Oriented Hypercubes

Abstract

In this article we investigate the existence of (2,3)-cordial labelings of oriented hypercubes. In this investigation, we determine that there exists a (2,3)-cordial oriented hypercube for any dimension divisible by 3. Next, we provide examples of (2,3)-cordial oriented hypercubes of dimension not divisible by 3 and state a conjecture on existence for dimension 3k + 1. We close by presenting the only 3D oriented hypercubes up to isomorphism that are not (2,3)-cordial.