Graceful labeling on torch graph

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 O_n is a graceful graph.