@article{Article_92,

title = {On Edge-Gracefulness of Wheel Graphs},

journal = {Communications in Combinatorics, Cryptography & Computer Science},

volume = {2024},

issue = {2},

issn = { 2783-5456 },

year = {2024},

url = {http://cccs.sgh.ac.ir/Articles/2024/issue 2/2-8-OnEdgeGracefulnessofWheelGraphs.pdf},

author = {Aaron DC. Angel and John Loureynz F. Gamurot and John Rafael M. Antalan and Richard P. Tagle},

keywords = {Graceful Labeling, Edge-graceful Labeling, Wheel Graph, Diophantine Equation},

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.}

};