Pelabelan Prima pada Kelas Graf Hasil Operasi Perkalian Tensor

Suci Triwahyuniti; Desi Rahmadani

doi:10.37905/jjom.v8i1.34596

Pelabelan Prima pada Kelas Graf Hasil Operasi Perkalian Tensor

Suci Triwahyuniti, Desi Rahmadani

Abstract

A graph with a vertex set is said to be a prime graph if there exists a bijective mapping , where denotes the number of vertices in , such that for any two adjacent vertices and in have . Tensor Product graph is a way to combine (compose) two graphs into one larger and more complex graph. The result is a new graph that reflects the connection properties of the two original graphs, but in a very specific and more complex way than other graph operations. Therefore, this research aims to determine whether there is prime labeling in the class of graphs resulting from the Tensor Product of the path graph and the cycle graph . The research employed analytical and exploratory methods with a trial-and-error strategy to determine the labeling that possesses a prime property. The results of this study prove that two classes of the Tensor Product graph for , and graph , for are prime graph. This finding expands the results on classes of graphs that admit prime labeling and provides a basis for further research on graph labeling in other graph operations

Keywords

Pelabelan Prima; Perkalian Tensor; Graf Cycle; Graf Path

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DOI: https://doi.org/10.37905/jjom.v8i1.34596