Dimensi Metrik Hasil Operasi Tertentu pada Graf Petersen Diperumum
Keywords:
Himpunan pembeda, dimensi metrik, graf Petersen diperumumAbstract
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.
Downloads
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. Baca, E.T. Baskoro, A.N.M. Salman, S.W. Saputro, and D. Suprijanto, “The metric dimension of regular bipartite graph”, Bulletin Mathematique de la Societe des Sciences Mathematiques 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,



