Graceful and &#961- &#770- labeling on the maximum A-star graph
H Sumardi (a*), A Susanta (a), Z Amri (b), Harizahayu (c)

a) Program Studi Magister Pendidikan Matematika, Universitas Bengkulu, Jl. W. R. Supratman, Kandang Limun, Muara Bangka Hulu, Bengkulu 38371, Indonesia
b) Program Studi Magister Pendidikan Matematika, PPs Universitas Muhammadiyah
Sumatera Utara, Jl. Denai No. 217, Kota Medan 20226, Indonesia
c) Politeknik Negeri Medan, Jl. Almamater NO.1 Kampus USU Medan

Abstract

A graph \(G(V,E)\) is called graceful graph if there is an injective mapping \(f\) from \(V(G)\) to \(\{0,1,...,|E|\}\) and bijective mapping \(f^\) from \(E(G)\) to \(\{1,2,...,|E|\}\) such that for each \(uv\in E(G)\) which \(u,v\in V(G)\), \(f^(uv)=|f(u)-f(v)|\), along with a modification graceful graph, namely \(\hat{\rho}\) labeling. The maximum A-star graph is formed of the alphabet A for which each vertex is assigned a star graph \((S_n)\). This paper purpose is to construct the formula of graceful and \(\hat{\rho}\) labeling on the maximum A-star graph.

Keywords: Graceful labeling- &#961- &#770- labeling- The maximum A-star graph

Topic: Mathematics