Bilangan Kromatik Lokasi pada Graf Hasil Amalgamasi Sisi dari Graf Bintang dan Graf Lengkap

  • Fiqih Hartiansyah Institut Sains dan Teknologi Annuqayah Sumenep
  • Darmaji Darmaji Institut Teknologi Sepuluh Nopember Surabaya
Keywords: bilangan kromatik lokasi, graf hasil amalgamasi sisi, graf bintang, graf lengkap

Abstract

The locating coloring of graph extends the vertex coloring dan partition dimension of graph. The minimum number of locating coloring of graph G is called the locating chromatic number of graph G. In this paper will discuss the locating chromatic number of edge amalgamation graph of star graph with order m+1 and complete graph with order n. The method used to obtain the locating chromatic number of graph is to determine the upper dan lower bound. The results obtained are that the locating chromatic number of edge amalgamation graph of star graph with order m+1 and complete graph with order n is  for  and .

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References

Asmiati, Assiyatun, H., Baskoro, E.T. (2011) Locating-Chromatic Number of Amalgamation of Stars, ITB J. Sci. 43 A(1):1-8.

Amalia, R., Firdausiyah, Yulianto, Tony., Faisol, Kuzairi. (2022) The Local Strong Metric Dimension in the Join of Graphs. Journal of Physics: Conference Series. 2157. 012004. https://doi.org/10.1088/1742-6596/2157/1/012004

Amalia, R., Mufidah, SA., Yulianto, Tony., Faisol, Kuzairi. (2021) The complement metric dimension of particular tree. Journal of Physics: Conference Series. 1836. 012011. https://doi.org/10.1088/1742-6596/1836/1/012011

Baskoro, E.T., Purwasih, I.A. (2012) The Locating-Chromatic Number for Corona Product of Graphs, Southeast-Asian J. of Sciences. 1(1):124-134.

Behtoei, A., Anbarloei, M. (2014) The locating chromatic number of the join of graphs, Bull. Iranian Math. Soc. 40(6):1491-1504.

Chartrand, G., Erwin, D., Henning, M.A., Slater, P.J., Zhang, P. (2002) The locating-chromatic number of a graph, Bull. Inst. Combin. Appl. 36:89-101.

Chartrand, G., Erwin, D., Henning, M.A., Slater, P.J., Zhang, P. (2003) Graphs of order n with locating-chromatic number n-1, Discrete Mathematics. 269:65-79.

Chartrand, G., Lesniak, L. (1996) Graphs & Digraphs, Chapman & Hall, London.

Chartrand, G., Salehi, E., Zhang, P. (2000) The partition dimension of a graph, Aequationes Mathematicae. 59:45-54.

Darmawahyuni, A., Narwen. (2016) Bilangan Kromatik Lokasi Dari Graf Ulat, Jurnal Matematika UNAND. 5(1):1-6.

Gross, J.L., Yellen, J. (2006) Graph Theory and its Applications, Chapman & Hall, Francis.

Hartsfield, N., Ringel G. (1990) Pearls in Graph Theory, Academic Press, London.

Marsudi (2016) Teori Graf, UB Press, Malang.

Nur, M., Welyyanti, D., Narwen. (2020) Bilangan Kromatik Lokasi Untuk Graf Pohon Pisang B_(n,k), Jurnal Matematika UNAND. 9(2):70-75.

Rahmatalia, S., Asmiati, Notiragayu. (2022) Bilangan Kromatik Lokasi Graf Split Lintasan, Jurnal Matematika Integratif. 18(1):73-80.

Silvia, M., Welyyanti, D., Efendi. (2018) Bilangan Kromatik Lokasi Pada Graf Lobster L_(n,m,1) Dengan n=2,3,4 Dan m=3, Jurnal Matematika UNAND. 7(3):94-103.

West, D.B. (2001) Introduction to Graph Theory, University of Illinois, Urbana.

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Abstract view : 418 times
Published
2023-07-26
How to Cite
Hartiansyah, F., & Darmaji, D. (2023). Bilangan Kromatik Lokasi pada Graf Hasil Amalgamasi Sisi dari Graf Bintang dan Graf Lengkap. Zeta - Math Journal, 8(2), 66-70. https://doi.org/10.31102/zeta.2023.8.2.66-70