The Graceful Labeling on W Graph
Kiki A. Sugeng Wed Giyarti · Journal of Hunan University · 2021
Let G be a graph with vertex set V = V (G) and edge set E = E(G) . Graceful labeling is an injective function g from the vertex set V to a set of number {0,1,2,…,| E |} which induces a bijective function g^' from the set E to the set of number {0,1,2,…,| E |}, where for each edge uv ∈ E with u,v ∈ V applies g' ( uv ) = |g( u )-g( v )|. A graph with graceful labeling is called a graceful graph. This research aims to construct a new graph, namely a W graph, and prove that the W graph is graceful. W graph is a graph constructed from two ladder graphs and one C 3 graph, where C 3 is formed by connecting the end vertices of each ladder, for example, v 1 and x 1 , and by adding a vertex connected to the vertices v 1 and x 1 . In this paper, the authors show that the W graph satisfies the graceful labeling so that the W graph is graceful. Keywords: graceful labeling, graph labeling, W graph.