Dimensi Metrik Campuran pada Graf Hasil Operasi Korona Dua Graf Terhubung

Azahra, Nadia (2022) Dimensi Metrik Campuran pada Graf Hasil Operasi Korona Dua Graf Terhubung. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Topik yang dijadikan bahan kajian dalam penelitian ini adalah dimensi metrik campuran. Dimensi metrik campuran merupakan penggabungan antara dua konsep pada teori graf yaitu dimensi metrik dan dimensi metrik sisi. Penelitian tentang dimensi metrik campuran belum banyak diteliti khususnya pada graf hasil operasi biner. Pada tesis ini, ditentukan dimensi metrik campuran dari graf hasil operasi korona dan dikembangkan algoritma untuk menentukan dimensi metrik campuran. Algoritma ini melakukan pengecekan untuk semua kombinasi dari himpunan $W$ yang memenuhi syarat himpunan pembeda campuran. Dimensi metrik campuran mula-mula dicari berdasarkan sebuah algoritma komputasi sampai diperoleh dugaan bentuk umum. Selanjutnya, dugaan ini dibuktikan secara analisis sehingga diperoleh bentuk umum dimensi metrik campuran pada graf hasil operasi korona dua graf terhubung sederhana.
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The topic that is used in this research namely mixed metric dimensions. Mixed metric dimensions is a new concept of metric dimension by combining two concepts in graph theory, namely metric dimension and edge metric dimension. Research on mixed metric dimension has not been widely studied, especially on graphs resulting from binary operations. In this thesis, we determine the mixed metric dimension of the graph resulting from the corona operation and an algorithm is built to determine the mixed metric dimensions. This algorithm checks for all combinations of the $W$ set that meet the mixed resolving set conditions. The mixed metric dimensions are first searched based on a computational algorithm until an estimate of the general form is obtained. Furthermore, this conjecture is proven analytically so that a general form of mixed metric dimensions is obtained on the corona operation result of two simple connected graphs.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	metric dimension, mixed metric dimension, mixed resolving set, corona operation, algorithm
Subjects:	Q Science > QA Mathematics > QA166 Graph theory
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44101-(S2) Master Thesis
Depositing User:	Nadia Azahra
Date Deposited:	22 Jun 2022 07:52
Last Modified:	31 Oct 2022 02:10
URI:	http://repository.its.ac.id/id/eprint/94918

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