Pelabelan L(2,1) pada Graf Sierpinski S(n,k)

Yuri Sagala, Susiana Susiana

Abstract


Labeling L (2; 1) on a graph G is the function f of the set of vertices V (G) to the set of all non-negative numbers so that │f (u) - f (w) │ ≥ 2 if d (u; w) = 1 and │f (u) - f (w)│ ≥ 1 if d (u; w) = 2. The labeling number L (2; 1) of a graph G is the smallest k number so G has labeling L (2; 1) with max {f (v): v Є V (G) g} = k. The Sierpinski Graph is a form of expansion graph specifically from a complete graph. This study shows labeling on Sierpinski graph using Chang-Kuo algorithm and obtained the values L (2; 1) {S (n; 2)} = 4 and the value of L (2; 1) {S (n; 3)} = 6 for n ≥ 2, with L (2; 1) {G} is the smallest maximum number labeling L (2; 1) from a graph G. [LABELING L(2,1) IN SIERPINSKI S(N,K)](J. Sains Indon., 42(1): 22-24, 2018)

Keywords:
Graph Labeling L(2,1), Sierpinski Graph


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References


Baca, M., dan Mirka, M., (2008), Super Edge-Antimagic Graph: A Wealth ofProblems and Solutions, Brown Walker Press Boca Raton, Florida.

Calamoneri, T., dan Petreschi (2009), L(2;1)-Labeling of Unigraphs, Department of Computer Science, 1–19.

Chang, G., dan Kuo, D., (1996), The L(2; 1)-Labeling Problem on Graphs, SIAMJ. Disc. Math, 9, 309–316.

Chartrand, G., dan Lesniak, L., (1996), Graphs and Digraphs, CRC Press, Florida,USA.

Chartrand, G., dan Zhang, P., (2009), Chromatic Graph Theory, CRC Press, USA.

Fu, H., dan Xie, D., (2010), Equitable L(2; 1)-labelings of Sierpinski graphs, Australasian Journal of Combinatorics, 46, 147–156.

Gravier, S.; Klavzar, S., dan Mollard, M., (2005), Codes and ˘ L(2; 1)-Labelings in Sierpinski Graphs, Taiwanese Journal of Matematics, 9(4), 671–681.

Gravier, S.; Kovse, M., dan Parreau, A., (2009), Generalized Sierpinski Graphs, ANR IDEA,

Griggs, J., dan Yeh, R., (1992), Labeling graphs with a condition at distance two, SIAM J. Discrete Math., 5(4), 586–595.

Hale, W., (1980), Frequency assignment: theory and application, Proc IEEE, 68, 1479–1514.

Klavzar, S., dan Milutinovi ˘ c, U., (1997), Graphs ´ S(n; k) and a Variant of The Tower of Hanoi Problem, Czechoslovak Math J., 47(122), 95–104.

Lipschutz, S., dan Lipson, M., (2007), Theory and Problems of Discrete Mathematics, McGraw-Hill, United States of America.

Marr, A., dan Wallis, W., (2001), Magic Graphs, Birkhauser, Boston.

Munir, R., (2003), Matematika Diskrit, Informatika Bandung, Bandung.

Paul, S.; Pal, M., dan Pal, A., (2014), L(2; 1)-labeling of Circular-arc Graph, Annalsof Pure and Applied Mathematics, 5(2), 208–219.

Rao, G., (2009), Discrete Mathematical Structures, New Age International, New Delhi.

Rosen, K., (2012), Discrete Mathematics and its Applications, McGraw-Hill, United States of America.

Shao, Z.; Yeh, R., dan Zhang, D., (2008), The L(2; 1)-labeling on graphs and the47 frequency assignment problem, Elsevier, 21, 37–41.

Siang, J., (2006), Matematika Diskrit dan Aplikasinya pada Ilmu Komputer, Andi, Bandung.

Vasudev, C., (2006), Graph Theory with Applications, New Age International, New Delhi.

Wallis, W., (2006), A Beginner’s Guide to Graph Theory, Birkhauser, Boston.




DOI: https://doi.org/10.24114/jsi.v42i1.12244

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