Soraya, Rafifah Safa Azmitha (2026) Dimensi Metrik Lokal Graf Lompat. Other thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Dimensi metrik lokal merupakan pengembangan dari konsep dimensi metrik dengan pembatasan pada titik-titik yang bertetangga dalam graf. Penelitian ini menentukan
dimensi metrik lokal pada graf lompat, yaitu graf yang merupakan komplemen dari graf garis. Graf lompat mentransformasi sisi-sisi graf asal menjadi titik-titik, dengan dua titik bertetangga jika dan hanya jika sisi-sisi yang berkorespondensi pada graf asal tidak memiliki titik ujung bersama.Tujuan penelitian ini adalah menentukan dimensi metrik dan dimensi metrik lokal dari graf lompat untuk beberapa kelas graf dasar dan graf hasil operasi korona. Graf dasar yang digunakan meliputi graf lintasan Pn, graf siklus Cn, graf lengkap Kn, dan graf bipartit lengkap Ka,b. Selain itu, penelitian juga mengonstruksi graf lompat dari graf khusus yaitu graf tangga Ln, graf jewel Jn, graf buku segi empat BEk, serta graf kipas Fn. Metode penelitian yang digunakan adalah konstruksi graf lompat, penentuan himpunan pembeda dengan kardinalitas minimum, dan pembuktian
matematis untuk memperoleh formula umum dimensi metrik lokal. Hasil penelitian diharapkan memberikan kontribusi teoretis dalam pengembangan teori graf khususnya pada dimensi metrik lokal dan graf transformasi, serta dapat menjadi rujukan untuk penelitian selanjutnya.
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Local metric dimension is an extension of the concept of metric dimension with restrictions on neighboring vertices in a graph. This study examines local metric dimension in jump graphs, which are graphs that are the complement of line graphs. A jump graph transforms the edges of the original graph into vertices, with two vertices being adjacent if and only if the corresponding edges in the original graph do not share a common endpoint. The objective of this study is to determine the metric dimension and local metric dimension of jump graphs for several classes of basic graphs and graphs resulting from corona operations. The basic graphs studied include the path graph Pn, the cycle graph Cn, the complete graph Kn, and the complete bipartite graph Ka,b. In addition, this study constructs the jump graphs of several special graphs, namely the ladder graph Ln, the jewel graph Jn, the quadrilateral book graph BEk, and the fan graph Fn. The research methods used are jump graph construction, determination of the minimum cardinality distinguishing set, and mathematical proof to obtain a general formula for local metric dimensions. The results of this study are expected to provide a theoretical contribution to the development of graph theory, particularly in local metric dimensions and transformation graphs, and can be used as a reference for further research
| Item Type: | Thesis (Other) |
|---|---|
| Uncontrolled Keywords: | dimensi metrik, dimensi metrik lokal, graf lompat, graf garis, komplemen graf, metric dimension, local metric dimension, jump graph, line graph, complement of graph |
| Subjects: | Q Science > QA Mathematics > QA166 Graph theory |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis |
| Depositing User: | Rafifah Safa Azmitha Soraya |
| Date Deposited: | 29 Jul 2026 01:11 |
| Last Modified: | 29 Jul 2026 01:11 |
| URI: | http://repository.its.ac.id/id/eprint/139364 |
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