Graceful labeling on torch graph

Jona Martinus Manulang, Kiki A. Sugeng

Abstract


Let G be a graph with vertex set V=V(G) and edge set E=E(G). An injective function f:V --> {0,1,2,...,|E|} is called graceful labeling if f induces a function f*(uv)=|f(u)-f(v)| which is a bijection from E(G) to the set {1,2,3,...,|E|}. A graph which admits a graceful labeling is called a graceful graph. In this paper, we show that torch graph On is a graceful graph.

Keywords


graceful graph; graceful labeling; torch graph

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References


P. Rachmandika and K. A. Sugeng, Super edge-magic total labeling of Torch Graph, Prosiding Seminar Nasional Matematika. (2014).

J.A. Gallian, A Dynamic Survey of Graph Labeling. The Electronic Journal of Combinatorics 5. (2012)

A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs (Internat. Symposium, Rome, July 1966), Gordon and Breach, N. Y. and Dunod Paris (1967) 349-355.




DOI: http://dx.doi.org/10.19184/ijc.2018.2.1.2

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ISSN: 2541-2205

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