DEKOMPOSISI GRAF POHON PISANG Bm,n - Aji Sailendra, Alfi Istijap; Alisah, Evawati; Nasichuddin, Achmad (Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang, 2022)
A decomposition of graph G is collection of subgraphs 〖H_i〗_(i=1)^n from G such that H_i [E_i] for E_i is a subset of E(G) and 〖E_i〗_(i=1)^n is a partition of E(G). The purpose of the research was to determine the decomposition of the banana tree graph B_(m,n), for m≥1 and n≥2. The research method used in this research is library research. The steps used to determine the decomposition of the banana tree graph B_(m,n) are as follow: (a) Draw a banana tree graph B_(m,n) and label each edge and vertex, (b) Determine the partition on the edges of the banana tree graph B_(m,n), (c) Induced subgraph of from partitions of the banana tree graph B_(m,n), (d) Determine the decomposition of the banana tree graph B_(m,n), (e) Tabulate a conjecture on the decomposition of the banana tree graph B_(m,n), (f) Construct theorem of the decomposition theorem of of the banana tree graph B_(m,n) and its proof. The result of the reasearch is with m≥1 and n≥2, because banana tree graph B_(m,n) is decomposed by the complete graph 〖mK〗_2-decomposition.