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Metric Dimension of Second Order Complete Graph with Honeycomb Network Cross Operation Product
Dimensi Metrik Graf Hasil Kali Graf Lengkap Orde Dua terhadap Graf Sarang Lebah
Jurnal Matematika, Statistika dan Komputasi
ISSN 2614-8811, 1858-1382
Published 2024-09-15
Publisher Department of Mathematics, Hasanuddin University
Language en
Abstract
English
Metric dimension is a concept in graph theory that has been developed in terms of the concept and its application. Let G be a connected graph and S be a vertex subset on connected graph G. The set S is called a resolving set for G if every vertex on graph G has a distinct representation of one to each other of S. A resolving set containing a minimum cardinality is called basis. The metric dimension on graph G is cardinality of basis on graph G, notated with dim (G). In this case, the cross-product graph will be used for the research. The aim of this research is to determine the metric dimension of the second order complete graph (K2) with honeycomb networks (HC(n)) cross-operation product. Utilizing mathematical induction, we generated dim(K2×HC(n)) = 3.
Bahasa Indonesia
Dimensi metrik merupakan konsep dalam teori graf yang terus dikembangkan dari segi konsep maupun penerapannya. Misalkan G adalah graf terhubung dan S adalah suatu subset titik pada graf terhubung G. Himpunan S disebut himpunan penentu pada G jika untuk setiap titik pada graf G memiliki representasi jarak yang berbeda terhadap S. Himpunan penentu dengan kardinalitas minimum disebut basis. Dimensi metrik graf G adalah kardinalitas basis dari graf G yang dinotasikan dengan dim (G). Pada penelitian ini disajikan hasil graf yang menggunakan operasi kali. Tujuan dari penelitian ini yaitu untuk menentukan dimensi metrik dari graf hasil operasi kali antara graf lengkap orde 2 (K2) terhadap graf sarang lebar (HC(n)). Menggunakan metode induksi matematika, diperoleh hasil pembahasan penelitian yaitu dim(K2×HC(n)) = 3.
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Metadata source: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai,
first harvested 5 Nov 2026,
last seen 5 Nov 2026.
Original metadata (oai_dc)
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<dc:title xml:lang="en">Metric Dimension of Second Order Complete Graph with Honeycomb Network Cross Operation Product</dc:title>
<dc:title xml:lang="id">Dimensi Metrik Graf Hasil Kali Graf Lengkap Orde Dua terhadap Graf Sarang Lebah</dc:title>
<dc:creator xml:lang="en">Jannah, Saskia Nurul </dc:creator>
<dc:creator xml:lang="en">Basir, Hasmawati</dc:creator>
<dc:creator xml:lang="en">Aris, Naimah </dc:creator>
<dc:subject xml:lang="en">metric dimension</dc:subject>
<dc:subject xml:lang="en">cross product graph</dc:subject>
<dc:subject xml:lang="en">complete graph</dc:subject>
<dc:subject xml:lang="en">honeycomb network</dc:subject>
<dc:subject xml:lang="en">Second Order Complete Graph with Honeycomb Network Cross Operation Product</dc:subject>
<dc:subject xml:lang="id">dimensi metrik</dc:subject>
<dc:subject xml:lang="id">graf produk hasil kali</dc:subject>
<dc:subject xml:lang="id">graf lengkap</dc:subject>
<dc:subject xml:lang="id">graf sarang lebah</dc:subject>
<dc:subject xml:lang="id">Graf Hasil Kali Graf Lengkap Orde Dua terhadap Graf Sarang Lebah</dc:subject>
<dc:description xml:lang="en">Metric dimension is a concept in graph theory that has been developed in terms of the concept and its application. Let G be a connected graph and S be a vertex subset on connected graph G. The set S is called a resolving set for G if every vertex on graph G has a distinct representation of one to each other of S. A resolving set containing a minimum cardinality is called basis. The metric dimension on graph G is cardinality of basis on graph G, notated with dim (G). In this case, the cross-product graph will be used for the research. The aim of this research is to determine the metric dimension of the second order complete graph (K2) with honeycomb networks (HC(n)) cross-operation product. Utilizing mathematical induction, we generated dim(K2×HC(n)) = 3.</dc:description>
<dc:description xml:lang="id">Dimensi metrik merupakan konsep dalam teori graf yang terus dikembangkan dari segi konsep maupun penerapannya. Misalkan G adalah graf terhubung dan S adalah suatu subset titik pada graf terhubung G. Himpunan S disebut himpunan penentu pada G jika untuk setiap titik pada graf G memiliki representasi jarak yang berbeda terhadap S. Himpunan penentu dengan kardinalitas minimum disebut basis. Dimensi metrik graf G adalah kardinalitas basis dari graf G yang dinotasikan dengan dim (G). Pada penelitian ini disajikan hasil graf yang menggunakan operasi kali. Tujuan dari penelitian ini yaitu untuk menentukan dimensi metrik dari graf hasil operasi kali antara graf lengkap orde 2 (K2) terhadap graf sarang lebar (HC(n)). Menggunakan metode induksi matematika, diperoleh hasil pembahasan penelitian yaitu dim(K2×HC(n)) = 3.</dc:description>
<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
<dc:date>2024-09-15</dc:date>
<dc:type>info:eu-repo/semantics/article</dc:type>
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<dc:format>application/pdf</dc:format>
<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/36329</dc:identifier>
<dc:identifier>10.20956/j.v21i1.36329</dc:identifier>
<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 21 No. 1 (2024): SEPTEMBER 2024; 255-266</dc:source>
<dc:source>2614-8811</dc:source>
<dc:source>1858-1382</dc:source>
<dc:language>en</dc:language>
<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/36329/12013</dc:relation>
<dc:relation>10.20956/j.v21i1.36329.g12013</dc:relation>
<dc:coverage xml:lang="en">Makassar, 2024</dc:coverage>
<dc:coverage xml:lang="id">Makassar, 2024</dc:coverage>
<dc:rights xml:lang="en">Copyright (c) 2024 Jurnal Matematika, Statistika dan Komputasi</dc:rights>
<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
</oai_dc:dc>
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APA 7
Jannah, S. N., Basir, H., & Aris, N. (2024). Metric Dimension of Second Order Complete Graph with Honeycomb Network Cross Operation Product. Jurnal Matematika, Statistika dan Komputasi, 21(1), 255–266. https://doi.org/10.20956/j.v21i1.36329
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IEEE
S. N. Jannah, H. Basir, and N. Aris, “Metric Dimension of Second Order Complete Graph with Honeycomb Network Cross Operation Product,” Jurnal Matematika, Statistika dan Komputasi, vol. 21, no. 1, pp. 255–266, 2024, doi: 10.20956/j.v21i1.36329.
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