Graceful labeling on torch graph

• Main Authors: Jona Martinus Manulang, Kiki A. Sugeng
• Format: Article
• Language: English
• Published: InaCombS; Universitas Jember; dan Universitas Indonesia 2018-06-01
• Series: Indonesian Journal of Combinatorics
• Subjects: graceful graph; graceful labeling; torch graph
• Online Access: http://www.ijc.or.id/index.php/ijc/article/view/33

Let G be a graph with vertex set V=V(G) and edge set E=E(G). An injective function f:V<span style="font-family: symbol;"> --&gt; </span>{0,1,2,...,|E|} is called graceful labeling if f induces a function f^*(uv)=|f(u)<span style="font-family: symbol;">-</span>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 O_n is a graceful graph.