(2,3)-Cordial Oriented Hypercubes
Jonathan M. Mousley, Manuel A. Santana, LeRoy B. Beasley, and David E., Brown
TL;DR
This paper explores the existence of (2,3)-cordial labelings in oriented hypercubes, establishing existence for dimensions divisible by 3, providing examples for other dimensions, and conjecturing about dimensions of the form 3k+1.
Contribution
It proves (2,3)-cordial labelings exist for all hypercube dimensions divisible by 3 and offers new examples and conjectures for other dimensions.
Findings
(2,3)-cordial hypercubes exist for all dimensions divisible by 3
Examples of (2,3)-cordial hypercubes are provided for non-divisible dimensions
Identifies non-(2,3)-cordial 3D hypercubes up to isomorphism
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.
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Taxonomy
TopicsInterconnection Networks and Systems · Graph Labeling and Dimension Problems · Advanced Graph Theory Research