Dimensi Bi-metrik Komplemen Graf Hasil Operasi Korona

Sundusia, Jafna Kamalia (2022) Dimensi Bi-metrik Komplemen Graf Hasil Operasi Korona. Masters thesis, Institut Tenologi Sepuluh Nopember.

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Abstract

Teori graf semakin berkembang pesat hingga saat ini. Salah satu perkembangan teori graf tentang himpunan pembeda yaitu dimensi bi-metrik yang merupakan pengembangan dari dimensi metrik. Pengembangan dari dimensi bi-metrik ini adalah penentuan representasi setiap titik v pada graf G terhadap himpunan pembeda, yaitu berupa k-tuple dari pasangan panjang lintasan terpendek dan panjang lintasan terpanjang antara titik v dan titik s_i,i∈{1,2,…,n} di himpunan pembeda. Pada penelitian ini dilakukan pengembangan terhadap himpunan pembeda bi-metrik yang disebut himpunan pembeda bi-metrik komplemen dari graf G, dan kemudian ditentukan yang kardinalitasnya maksimum, yaitu dimensi bi-metrik komplemen pada graf G, (β_b ) ̅(G). Tujuan dari penelitian ini adalah memperkenalkan varian baru dari dimensi bi-metrik pada graf dan menganalisisnya lebih lanjut, serta menentukan dimensi bi-metrik komplemen dari graf hasil operasi korona dua graf terhubung G dan H, (β_b ) ̅(G⊙H). Dari penelitian ini diperoleh (β_b ) ̅(G⊙H) untuk G dan H masing-masing adalah graf lengkap, graf lintasan, graf bintang, dan graf siklus.
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Graph theory is growing rapidly until now. One of the developments in graph theory regarding the resolving set is the bi-metric dimension, which is the development of the metric dimension. The development of this bi-metric dimension is to determine the representation of each vertex v in graph G to the resolving set, which is in the form of k-tuples from pair of the shortest path length and the longest path length between vertex v and vertex s_i,i∈{1,2,…,n} in the resolving set. In this research, the development of the bi-metric resolving set is called the complement bi-metric resolving set of graph G, and then the maximum cardinality is determined, namely the complement bi-metric dimension in graph G, (β_b ) ̅(G). The purpose of this study is to introduce a new variant of the bi-metric dimension in the graph and analyze it further, as well as determine the complement bi-metric dimension of corona product graph G and H is notated (β_b ) ̅(G⊙H). From this research is gained (β_b ) ̅(G⊙H) for G and H are complete graph, path graph, star graph, and cycle graph.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Dimensi metrik, dimensi bi-metrik, graf hasil operasi korona, dimensi bi-metrik komplemen.Metric dimension, bi-metric dimension, corona product graph, complement bi-metric dimension.
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA166 Graph theory
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44101-(S2) Master Thesis
Depositing User:	Jafna Kamalia Sundusia
Date Deposited:	10 Feb 2022 01:30
Last Modified:	02 Nov 2022 03:57
URI:	http://repository.its.ac.id/id/eprint/93398

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