Dimensi Metrik Dari Graf Jaring Laba-Laba
DOI:
https://doi.org/10.30605/proximal.v5i2.1788Keywords:
Dimensi Metrik, Graf Jaring Laba-LabaAbstract
Dimensi metrik dari graf terhubung G adalah kardinalitas dari himpunan pembeda minimum dari G, dimana W disebut himpunan pembeda dari G jika r(v|W) berbeda untuk setiap v di V(G). Penelitian ini bertujuan untuk menentukan dimensi metrik dari graf jaring laba-laba R_(m,n). Graf jaring laba-laba dikonstruksi dari graf bintang S_n sebanyak 1 dan graf sikel C_n sebanyak m. Konstruksi graf tersebut melibatkan definisi dari C_n(m) yang menyatakan graf sikel C_n ke-m , dengan V(C_n(m)) = {a_(m1), a_(m2), ..., a_(mn)} dan V(S_n) = {u, a_(m1), a_(m2), ..., a_(mn)} dengan u sebagai titik pusatnya, dimana m di N dan n lebih dari atau sama dengan 3 . Dari hasil penelitian, diperoleh dimensi metrik dari graf jaring laba-laba R_(m,n) adalah 3.
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References
Ali, M., Rahim, M. T., & Ali, G. (2012). On two families of graphs with constant metric dimension. Journal of Prime Research in Mathematics, 8(January), 95–101.
Bača, M., Baskoro, E. T., Salman, A. N. M., Saputro, S. W., & Suprijanto, D. (2011). The metric dimension of regular bipartite graphs. Bulletin Mathématique de La Société Des Sciences Mathématiques de Roumanie, 54 (102)(1), 15–28. http://www.jstor.org/stable/43679200
Chartrand, G., Eroh, L., Johnson, M. A., & Oellermann, O. R. (2000). Resolvability in graphs and the metric dimension of a graph. Discrete Applied Mathematics, 105(1), 99–113. https://doi.org/https://doi.org/10.1016/S0166-218X(00)00198-0
FITRIANI, F., & CAHYANINGTIAS, S. (2021). Graf Dual Antiprisma Dan Dimensi Metriknya. E-Jurnal Matematika, 10(1), 6. https://doi.org/10.24843/mtk.2021.v10.i01.p313
Ilmayasinta, N. (2019). Dimensi Metrik Pada Graf Buku Ganda. Vygotsky, 1(1), 21. https://doi.org/10.30736/vj.v1i1.89
Iswadi, H., Baskoro, E. T., Salman, A. N. M., & Simanjuntak, R. (2010). The resolving graph of amalgamation of cycles. Utilitas Mathematica, 83, 121–132.
Khoiriah, S., & Kusmayadi, T. A. (2018). Dimensi Metrik Lokal Pada Graf Antiprisma Dan Graf Sun. Journal of Mathematics and Mathematics Education, 8(1), 9–15. https://doi.org/10.20961/jmme.v8i1.25816
Melter, F. H., & Harary, F. (1976). On the metric dimension of a graph. Ars Combin, 2, 191–195.
Noprianilubis, J., Panjaitan, A., Surya, E., & Syahputra, E. (2017). Analysis Mathematical Problem Solving Skills of Student of the Grade VIII-2 Junior High School Bilah Hulu Labuhan Batu. 4(2), 131–137.
Saifudin, I. (2016). Dimensi Metrik dan Dimensi Partisi dari Famili Graf Tangga. Justindo, 49, 105–112. http://repository.unmuhjember.ac.id/91/1/DAFTAR ARTIKEL PENELITIAN ILHAM SAIFUDIN.pdf
Slater, P. J. (1975). Leaves of trees. Congr. Numer, 14(549–559), 37.
Sukmawati, S., & Amelia, R. (2020). Analisis kesalahan siswa smp dalam menyelesaikan soal materi segiempat berdasarkan teori nolting 1,2. 3(5), 423–432. https://doi.org/10.22460/jpmi.v3i5.423-432
Bača, M., Baskoro, E. T., Salman, A. N. M., Saputro, S. W., & Suprijanto, D. (2011). The metric dimension of regular bipartite graphs. Bulletin Mathématique de La Société Des Sciences Mathématiques de Roumanie, 54 (102)(1), 15–28. http://www.jstor.org/stable/43679200
Chartrand, G., Eroh, L., Johnson, M. A., & Oellermann, O. R. (2000). Resolvability in graphs and the metric dimension of a graph. Discrete Applied Mathematics, 105(1), 99–113. https://doi.org/https://doi.org/10.1016/S0166-218X(00)00198-0
FITRIANI, F., & CAHYANINGTIAS, S. (2021). Graf Dual Antiprisma Dan Dimensi Metriknya. E-Jurnal Matematika, 10(1), 6. https://doi.org/10.24843/mtk.2021.v10.i01.p313
Ilmayasinta, N. (2019). Dimensi Metrik Pada Graf Buku Ganda. Vygotsky, 1(1), 21. https://doi.org/10.30736/vj.v1i1.89
Iswadi, H., Baskoro, E. T., Salman, A. N. M., & Simanjuntak, R. (2010). The resolving graph of amalgamation of cycles. Utilitas Mathematica, 83, 121–132.
Khoiriah, S., & Kusmayadi, T. A. (2018). Dimensi Metrik Lokal Pada Graf Antiprisma Dan Graf Sun. Journal of Mathematics and Mathematics Education, 8(1), 9–15. https://doi.org/10.20961/jmme.v8i1.25816
Melter, F. H., & Harary, F. (1976). On the metric dimension of a graph. Ars Combin, 2, 191–195.
Noprianilubis, J., Panjaitan, A., Surya, E., & Syahputra, E. (2017). Analysis Mathematical Problem Solving Skills of Student of the Grade VIII-2 Junior High School Bilah Hulu Labuhan Batu. 4(2), 131–137.
Saifudin, I. (2016). Dimensi Metrik dan Dimensi Partisi dari Famili Graf Tangga. Justindo, 49, 105–112. http://repository.unmuhjember.ac.id/91/1/DAFTAR ARTIKEL PENELITIAN ILHAM SAIFUDIN.pdf
Slater, P. J. (1975). Leaves of trees. Congr. Numer, 14(549–559), 37.
Sukmawati, S., & Amelia, R. (2020). Analisis kesalahan siswa smp dalam menyelesaikan soal materi segiempat berdasarkan teori nolting 1,2. 3(5), 423–432. https://doi.org/10.22460/jpmi.v3i5.423-432
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Published
2022-08-02
How to Cite
Tuhfatul Janan, & Syifaul Janan. (2022). Dimensi Metrik Dari Graf Jaring Laba-Laba. Proximal: Jurnal Penelitian Matematika Dan Pendidikan Matematika, 5(2), 181–190. https://doi.org/10.30605/proximal.v5i2.1788
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