Original Research Article

Article volume = 2024 and issue = 2

Pages: 213–219

Article publication Date: December 06, 2024

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On Edge-Gracefulness of Wheel Graphs

Aaron DC. Angel(a,*), John Loureynz F. Gamurot(a), John Rafael M. Antalan(b), Richard P. Tagle(b)

(a) Alumni, Department of Mathematics and Physics, College of Science, Central Luzon State University (3120), Science City of Muñoz, Nueva Ecija, Philippines

(b) Faculty, Department of Mathematics and Physics, College of Science, Central Luzon State University (3120), Science City of Muñoz, Nueva Ecija, Philippines

Abstract:

In this paper, we present a complete proof that $W_3$ is the only edge-graceful wheel graph; a result that first appeared in the published work of S.Venkatesan and P.Sekar in 2017. Particularly, we first discuss the results of S.Venkatesan and P.Sekar, regarding the edge-gracefulness of wheel graphs, highlighting a point for improvement to their proof that $W_3$ is the only edge-graceful wheel graph. We then provide a complete proof of their result using the concepts of divisibility and Diophantine equations. We end the paper by giving some future works, related to edge-graceful labeling.

Keywords:

Graceful Labeling, Edge-graceful Labeling, Wheel Graph, Diophantine Equation

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Cite this article as:
  • Aaron DC. Angel, John Loureynz F. Gamurot, John Rafael M. Antalan, Richard P. Tagle, On Edge-Gracefulness of Wheel Graphs, Communications in Combinatorics, Cryptography & Computer Science, 2024(2), PP.213–219, 2024
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