Dimensi Metrik Hasil Operasi Tertentu pada Graf Petersen Diperumum

Asmiati Asmiati, Ahmad Ari Aldino, Notiragayu Notiragayu, La Zakaria, Muslim Anshori

Abstract


Misalkan  graf terhubung dan , , jarak titik  dan  yang  dinotasikan dengan  adalah panjang lintasan terpendek dari kedua titik tersebut. Misalkan  representasi titik  terhadap  adalah urutan   −vektor,   . Himpunan  disebut himpunan pembeda,  jika  untuk setiap dua titik berbeda , . Kardinalitas minimum dari himpunan pembeda  disebut dimensi metrik dari  dinotasikan dengan . Pada penelitian ini dibahas tentang dimensi metrik dari hasil operasi tertentu pada graf Petersen diperumum.

Keywords


himpunan pembeda; dimensi metrik; graf Petersen diperumum

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References


P.J. Slater., “Leaves of Trees,” in Proc. 6th Southeastern Conf. on Combinatorics, Graph Theory, and Computing, Congressus Numerantium, vol. 14, pp 549-559, 1975.

G. Chartrand, L. Eroh, M. A. Johnson, and O.R. Oellermann, “Resolvability in graphs and the metric dimension of a graph,” Discrete Applied Mathematics vol. 105, pp. 99–113, 2000.

C. Hernando, M. Mora, I.M. Pelayo, C. Seara, and D.R. Wood, “Extremal graph theory for metric dimension and diameter,”Electronic Journal of Combinatorics, vol. 17(30), pp.1-28, 2010.

M. Bača, E.T. Baskoro, A.N.M. Salman, S.W. Saputro, and D. Suprijanto, “The metric dimension of regular bipartite graph”, Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie, vol. 54 (102), pp. 15-28, 2011.

S.W. Saputro, E.T. Baskoro, A.N.M. Salman, and D. Suprijanto, “The metric dimension of a complete n-partite graph and its Cartesian product with a path,” Journal of Combinatorial Mathematics and Combinatorial Computing, vol. 71, pp. 283-293, 2009.

M. E. Watkins, “A Theorem on Tait Colorings with an Application to the Generalized Petersen Graphs,” J. Comb. Theory, vol. 164, pp. 152–164, 1969.

S. Ahmad, M. A. Chaudhry, I. Javaid, and M. Salman, “On The Metric Dimension of Generalized Petersen Graph”, Quastiones Mahematicae, vol.36, pp.421-435, 2013.

M. Imran, A. Q. Baig, M. K. Shafiq, M.K, and I. Tomecu,, “On Metric Dimension of Generalized Petersen Graph”, Ars Combinatoria, vol.117, pp. 113-130, 2014.

Mulyono and Wulandari, “The Metric Dimension of Friendship Graph F_n, Lollipop Graph L_(m,n) and Petersen Graph P_(n,m),” Bulletin of Mathematics. vol. 08, pp.117-124, 2016.




DOI: http://dx.doi.org/10.12962/limits.v16i2.5594

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Limits: Journal Mathematics and its Aplications by Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at https://iptek.its.ac.id/index.php/limits.