Dimensi Metrik Monofonik Sisi Pada Graf

Bimolo, Ana Diana Silvana (2026) Dimensi Metrik Monofonik Sisi Pada Graf. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Dimensi metrik monofonik sisi merupakan konsep dalam teori graf yang merupakan pengembangan dari dimensi metrik sisi dengan menggunakan jarak monofonik antara simpul dan sisi. Jarak monofonik antara simpul dan sisi didefinisikan sebagai nilai minimum dari jarak monofonik simpul ke kedua ujung sisi tersebut. Berdasarkan konsep ini, diperkenalkan himpunan pembeda monofonik sisi, yaitu himpunan simpul yang dapat membedakan setiap pasangan sisi melalui representasi jarak monofoniknya pada graf terhubung G. Kardinalitas minimum dari himpunan tersebut disebut dimensi metrik monofonik sisi, dinotasikan dengan emdim(G). Dalam penelitian ini diperoleh nilai eksak dari dimensi metrik monofonik sisi graf khusus yaitu graf lintasan P_n, graf siklus C_n, graf lengkap K_n, dan graf bipartit lengkap K_{p,q}, serta dimensi metrik monofonik sisi graf korona G\odot H, G\odot K_1, dan K_1 \odot H, dimana graf G dan H adalah elemen dari graf khusus. Selain itu diberikan karakterisasi dari dimensi metrik monofonik sisi dan membandingkan dimensi metrik monofonik sisi dan dimensi metrik sisi yang diperoleh emdim(G)<= edim}(G). Penelitian ini diharapkan dapat memberikan kontribusi dalam pengembangan teori graf dan topik dimensi metrik menggunakan konsep jarak monofonik.
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The edge monophonic metric dimension is a concept in graph theory that extends the notion of edge metric dimension by employing the monophonic distance between a vertex and an edge. The monophonic distance between a vertex and an edge is defined as the minimum of the monophonic distances from the vertex to the two end vertices of the edge. Based on this concept, the edge monophonic resolving set is introduced, which is a set of vertices that distinguishes every pair of edges through their monophonic distance representations in a connected graph G. The minimum cardinality of such a set is called the edge monophonic metric dimension, denoted by emdim(G). In this study, the exact values of the edge monophonic metric dimension are determined for several classes of graphs, namely path graphs P_n, cycle graphs C_n, complete graphs K_n, and complete bipartite graphs K_{p,q}. In addition, the edge monophonic metric dimension is investigated for corona graphs G \odot H, G \odot K_1, and K_1 \odot H, where G and H belong to special classes of graphs. Furthermore, a characterization of the edge monophonic metric dimension is provided, along with a comparison between the edge monophonic metric dimension and the edge metric dimension, showing that emdim(G) <= edim(G). This research is expected to contribute to the development of graph theory, particularly in the study of metric dimension based on monophonic distance.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Graf, Graf Korona, Jarak Monofonik, Dimensi Metrik Sisi, Himpunan Pembeda Monofonik Sisi, Dimensi Metrik Monofonik Sisi Graph, Corona Graph, Monophonic Distance, Edge Metric Dimension, Edge Monophonic Resolving Set, Edge Monophonic Metric Dimension
Subjects:	Q Science > QA Mathematics > QA166 Graph theory
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44101-(S2) Master Thesis
Depositing User:	Ana Diana Silvana Bimolo
Date Deposited:	21 Jul 2026 01:26
Last Modified:	21 Jul 2026 01:26
URI:	http://repository.its.ac.id/id/eprint/135950

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