A C3 Magic Decomposition on Friendship Graph with Odd Order

Indah Chairun Nisa; Sigit Pancahayani; Annisa Rahmita Soemarsono

doi:10.19184/jid.v23i1.23266

Indah Chairun Nisa Program Studi Matematika, Jurusan Matematika dan Teknologi Informasi, Institut Teknologi Kalimantan
Sigit Pancahayani Program Studi Statistika, Jurusan Matematika dan Teknologi Informasi, Institut Teknologi Kalimantan
Annisa Rahmita Soemarsono Program Studi Matematika, Jurusan Matematika dan Teknologi Informasi, Institut Teknologi Kalimantan

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

Abstract

Let G = (V,E) is graph with a non-empty set V containing vertices and a set of edges E. Also note that if H = {H_i⊆G_i = 1,2,3,...,n} is a collection of subgraphs from G with H_i≅H_j,i ≠ j. If H_i ∩ H_j = ∅ and ⋃ⁿ(i-1)H_i = G, then graph G admits a decomposition H. Furthermore, if there are f(v) and g(e) which are vertices and edges labeling at G, the total weight of each subgraph H_i,i = 1,2,3,…,n has the same value, namely ∑_(v∈V(H_i))▒〖f(v)〗+∑_(e∈E(H_i))▒〖g(e)〗= w, then the graph G contains the magic H_i decomposition with w as the magic constant. This research shows that the friendship graph F_n with n = 2k + 1 for k∈N admits a magic -(a,d)-C_3 decomposition with a magic constant w of 29dk + 6a + 15d.

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