Indah Chairun Nisa

Program Studi Matematika, Jurusan Matematika dan Teknologi Informasi, Institut Teknologi Kalimantan, Indonesia

Sigit Pancahayani

Program Studi Statistika, Jurusan Matematika dan Teknologi Informasi, Institut Teknologi Kalimantan, Indonesia

Annisa Rahmita Soemarsono

Program Studi Matematika, Jurusan Matematika dan Teknologi Informasi, Institut Teknologi Kalimantan, Indonesia

DOI: https://doi.org/10.19184/jid.v23i1.23266

ABSTRACT 

Let = ( , ) is graph with a non-empty set containing vertices and a set of edges . Also note that if = { ⊆ = 1,2,3, . . . , } is a collection of subgraphs from with ≅ , ≠ . If ∩ = ∅ and ⋃ = , then graph admits a decomposition . Furthermore, in this paper we define a new concept of labeling, that is tiered labeling which labels or to a label set containing arithmetic sequences with the smallest element and difference . If ( ) and ( ) are respectively vertices and edges labeling at and the total weight of each subgraph , =

1,2,3,…, has the same value, namely Σ ∈ ( ) ( ) + Σ ∈ ( ) ( ) = , then the graph contains a magic decomposition with as the magic constant. This research shows that using total tiered labeling, the friendship graph with = 2 + 1 for ∈ admits a magic decomposition with a magic constant = 29 + 6 + 15 .

Keywords: cyclic, friendship graph, arithmetic labeling, magic decomposition.