Dimensi Metrik dari Graf Jaring Laba-Laba
DOI:
https://doi.org/10.26555/konvergensi.v9i1.23336Abstract
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 elemen 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_(m3), ..., a_(mn)} dan V(S_n)={u, a_(m1), a_(m2), a_(m3), ..., a_(mn)}  dengan u sebagai titik pusatnya, dimana m elemen N dan n>3 . Dari hasil penelitian, diperoleh  dimensi metrik dari graf jaring laba-laba R_(m,n) adalah 3.
References
S. Sukmawati dan R. Amelia, “Analisis Kesalahan Siswa SMP Dalam Menyelesaikan Soal Materi Segiempat Berdasarkan Teori Nolting,†Jurnal Pembelajaran Matematika Inovatif, vol. 3, no. 5, pp. 423–432, 2020.
E. Setiawan dan S. Rizki, “Pengembangan Bahan Ajar Barisan dan Deret Matematika Berbasis Multimedia Interaktif,†Aksioma, vol 7, no. 3, pp. 456–472, 2018.
L, J. Nopriani, A. Panjaitan, E. Surya, and E. Syahputra, “Analysis Mathematical Problem Solving Skills of Student of the Grade VIII-2 Junior High School Bilah Hulu Labuhan Batu,†International Journal of Novel Research in Education and Learning, vol. 4. no. 2, pp. 131-137, 2017.
J. L. Gross, I. F. Khan, and M. I. Poshni, "Genus Distribution of Graph Amalgamation: Pasing at Root-vertices," Ars. Combinatoria, vol. 94, pp. 33-35, 2010.
P. J. Slater, "Leaves and Trees," Congr. Numer, vol. 14, pp. 549-559, 1975.
F. Harary and R. A. Melter, "On the Metric Dimension of a Graph," Ars Combin, vol. 2, pp. 191 – 195, 1976.
Chartrand, Eroh, Johnson, and Oellerman, "Resolvability in Graph and The Metric Dimension of A Graph," Discrete Applied Mathematics, vol. 105, pp. 99 – 113, 2000.
H. Iswadi, E. T. Baskoro, A. N. M. Salman, and R. Simanjuntak, "The Resolving Graph of Amalgamation of Cycles," Utilities Mathematica, vol. 83, pp. 121-132, 2010.
P. G. D. Gumilar, "Dimensi Metrik pada Graf Lobster L_n (q;r)," E-Jurnal Matematika, vol. 2, no. 2, pp. 43 – 48, 2013.
F. Fitriani, dan S. Cahyaningtias, "Graf Dual Antiprisma dan Dimensi Metriknya," E-Jurnal Matematika, vol. 10, no. 1, pp. 6 – 11, 2021.
M. Baca, E. T. Baskoro, A. N. M. Salman, S. W. Saputro, and D. Suprijanto, "The Metric Dimension of Regular Bipartite Graphs," Bull. Math. Soc. Math. Roumanie Tome, no. 1, pp. 15-28, 2011.
N. Ilmayasinta, "Dimensi Metrik pada Graf Buku Ganda," Jurnal Pendidikan Matematika dan Matematika, vol. 1, no. 1, pp. 21-27, 2019.
S. Khoiriah dan T. A. Kusmayadi, "Dimensi Metrik Lokal pada Graf Antiprisma dan Graf Sun," Journal of Mathematics and Mathematics Education, vol. 8, no. 1, pp. 9-15, 2018.
I. Saifudin, "Dimensi Metrik dan Dimensi Partisi dari Famili Graf Tangga," JUSTINDO, Jurnal Sistem & Teknologi Informasi Indonesia, vol. 1, no. 2, pp. 105-112, 2016.
M. Ali, G. Ali, U. Ali, and M. T. Rahim, "On Cycle Related Graphs with Constant Metric Dimension," Open Journal of Discrete Mathematics, vol. 2, pp. 21-23, 2012.
W. N. Sholihah, "Dimensi Metrik dan Non-Isolated Resolving Number pada Beberapa Graf Khusus," Jember: Digital Repository Universitas Jember, 2016.
R. N. Putra, L. Yulianti, dan S. SY, (2018). "Dimensi Metrik dari Graf W_n+C_n untuk
n 3,4," Jurnal Matematika UNAND, vol. 7, no. 2, pp. 165 – 169, 2018.
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