Pewarnaan Total pada Graf Bintang Sierpinski

Siti Khabibah, Dita Anies Munawwaroh

Abstract


Bilangan kromatik total graf G adalah bilangan bulat terkecil k dimana titik-titik dan sisi-sisi graf G dapat diwarnai dengan k warna sedemikian hingga dua titik yang adjecent dan sisi yang insiden dengan titik-titik tersebut diberikan warna yang berbeda.  Dalam paper ini dibahas mengenai pewarnaan total pada Graf Bintang Sierpinski, . Bilangan kromatik untuk pewarnaan total pada Graf ssn adalah 1 untuk n=1 dan 1+3.2n-2 untuk n>=2


Keywords


Sierpinski Star Graph; Total Coloring; Total chromatic number

Full Text:

PDF

References


Klavzar, S., Milutinovic, U.: Graphs S(n,k) and a Variant of the Tower of Hanoi Problem. Czechoslovak Math. J. 47 (122) (1997), 95–104

Teguia,A.M. dan Godbole, A.P., Sierpinski Gasket graphs and some of their properties, Australas. J. Combin. 35 (2006),181-192.

Xue, B., Zuo, L. dan Li, G., Coloring the Square of Sierpinski graphs, Graphs and Combinatorics, 31 (5) (2015), 1795-1805.

Hinz, A.M., Klavzar, S., Zemljic, S.S., A survey and slassification of Sierpinski-type graphs. Discrete Applied Mathematics. 217 (3) (2017). 565-600.

Hasunuma, T. Constructions of universalized Sierpinski graphs based on labeling manipulations. Electronic Notes in Discrete Mathematics. 60(2017) 47-54.

Klavzar, S., Coloring Sierpinski Graphs and Sierpinski Gasket Graphs, Taiwanese Journal of Mathematics, 12 (2) (2008),513-522.

Jakovac, M., Klavžar, S.: Vertex, edge, and total-toloring of Sierpiński-like graphs. Discrete Math. 309(2009), 1548–1556.

Hinz, A.M., Parisse, D., Coloring Hanoi and Sierpinski graphs. Discrete Mathematics. 312 (2012) 1521-1535.

Geetha, J., Somasundaram, K. Total coloring of generalized Sierpinski graphs. Australian Journal of Combinatorics.63 (1) (2015) 58-69.

Bresar, B., Ferme, J., Packing coloring of Sierpinski-type graphs. Aequationes Mathematicae. 92 (2018) 1091-1118.

Khabibah, S. Pewarnaan pada Graf Bintang Sierpinski. Jurnal Ilmiah Matematika dan Pendidikan Matematika. 9 (1) (2017) 37-43.

Vizing, V., G. On an estimate of the chromatic class of a p-graph, Diskret. Analiz. 3 (1964) 25–30




DOI: http://dx.doi.org/10.12962/limits.v18i2.6665

Refbacks

  • There are currently no refbacks.


Jumlah Kunjungan:

Creative Commons License
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.