arXiv subjects

LeRoy B. Beasley

Publications and source records attributed to LeRoy B. Beasley.

2 recordsLinked to original sources

arXiv2023

(2,3)-Cordial Oriented Hypercubes

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.

math.CO↗

arXiv2022

Cordial Digraphs

A $(0,1)$-labeling of a set is said to be friendly if the number of elements of the set labeled 0 and the number labeled 1 differ by at most 1. Let $g$ be a labeling of the edge set of a graph that is induced by a labeling $f$ of the vertex set. If both $g$ and $f$ are friendly then $g$ is said to be a cordial labeling of the graph. We extend this concept to directed graphs and investigate the cordiality of directed graphs. We show that all directed paths and all directed cycles are cordial. We also discuss the cordiality of oriented trees and other digraphs.

math.CO↗