The Graceful Labeling on W Graph

Wed Giyarti, Kiki A. Sugeng, Fery Firmansah


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 uvE with u,vV 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 C3 graph, where C3 is formed by connecting the end vertices of each ladder, for example, v1 and x1, and by adding a vertex connected to the vertices v1 and x1. 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.

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