Pelabelan Prima pada Graf Simpul Semi Total dari Graf Sikat

Dany Riansyah Putra; Mariatul Kiftiah; Fransiskus Fran

doi:10.26737/var.v5i2.2699

Pelabelan Prima pada Graf Simpul Semi Total dari Graf Sikat

Dany Riansyah Putra, Mariatul Kiftiah, Fransiskus Fran

Abstract

Artikel ini membahas mengenai pelabelan prima pada suatu graf sederhana dengan himpunan simpul dan himpunan sisi . Suatu graf adalah graf prima jika terdapat pemetaan bijektif sedemikian sehingga untuk setiap simpul dan yang bertetangga berlaku FPB. Selanjutnya, untuk graf sederhana yang berupa graf simpul semi total dari graf sikat, dikonstruksi suatu pelabelan prima dengan pembuktiannya memanfaatkan algoritma Euclidean. Hasil konstruksi menunjukkan bahwa graf simpul semi total dari graf sikat merupakan graf prima.

Kata Kunci:

Pemetaan; Graf Prima; Relatif Prima; Faktor Persekutuan Terbesar

Prime Labeling for a Semi-Total Point Graph of a Brush Graph

ABSTRACT

In this article, we investigate prime labeling for a simple graph G, where V(G) and E(G) are vertex set and edge set of G, respectively. A graph G is called a prime graph if there exists a bijective mapping such that for each u and v are adjacent vertices in G then we have GCD. Furthermore, in terms of a semi-total point graph of a brush graph, a prime labeling was constructed using the Euclidean algorithm. As a result, this graph was a prime graph.

Keywords

Mapping; Prime Graph; Relatively Prime; Greatest Common Divisor

Full Text:

PDF

References

Burton, D. M. (2007). Elementary Number Theory - Sixth Edition. Elementary Number Theory, 13–32.

Chaurasiya, M., Limda, A., Parmar, N., & Rupani, M. (2021). Note On k-Prime Labeling of Some Graphs. IRE Journals, 4(12), 2456-8880.

Edward, Samuel, A., & Kalaivani, S. (2016). Prime labeling for some octopus related graphs. International Organisation of Scientific Research (IOSR)-Journal of Mathematics, 12(6).

Fran, F., Putra, D. P., & Pasaribu, M. (2021). Prime Labeling of Line and Splitting Graph of Brush Graph. Journal of Physics: Conference Series, 2106.

Jog, S. R., Hande, S. P., Gutman, I., & Burcu Bozkurt, Ş. (2012). Derived graphs of some graphs. Kragujevac Journal of Mathematics, 36(2), 309–314.

Kavitha, P. (2022). Highly Total Prime Labeling for Some Duplicate Graph. TWMS J. AND ENG. MATH, 12(4), 1336-1348.

Lakshmi, R. A., Jayalakshmi, K., & Madhavi, T. (2018). Prime labeling of Jahangir graphs. International Journal of Engineering and Technology(UAE), 7(4.10 Special Issue 10), 389–392. https://doi.org/10.14419/ijet.v7i4.10.20944

Munir, R. (2010). Matematika Diskrit Ed ke-3. Bandung: Informatika.

Parthiban, A., Pir, A. A., & Felix, A. (2020). Certain Result on Prime and Prime Distance Labeling of Graphs. Journal of Physics: Conference Series. 1531.

Prajapati, U. M., & Gajjar, S. J. (2014). Some results on prime labeling. Open Journal of Discrete Mathematics, 4(3), 60–66.

Rahmawati, D., Fran, F., Yudhi, & Krisantoni, D. (2020). Total rainbow connection number of-centipede graph and its line, square, and middle graph. In AIP Conference Proceedings (Vol. 2268). https://doi.org/10.1063/5.0016815

Samuel, A. E., & Kalaivani, S. (2018). Prime Labeling to Drums Graphs. Annals of Pure and Applied Mathematics, 16(2), 307–312. https://doi.org/10.22457/apam.v16n2a7

Samuel, A. E., & Kalaivani, S. (2018a). Prime Labeling for Some Lilly related Graphs. International Journal of Pure and Applied Mathematics, 118(23), 195–204.

Samuel, A. E., & Kalaivani, S. (2018b). Prime Labeling to Brush Graphs. International Journal of Mathematics Trends and Technology, 55(4), 259–262. https://doi.org/10.14445/22315373/ijmtt-v55p533

Teresa, A. S., & Vijayalakshmi, G. (2019). k-Prime Labeling of Certain Cycle Connected Graphs. Malaya Journal of Matematik, S(1), 280-283.

Teresa, A. S., & Vijayalakshmi, G. (2020). k-Prime Labeling of One Point Union of Path Graph. Procedia Computer Science, 172, 649-654.

Vaidya, S. K., & Prajapati, U. M. (2011). Some Result on Prime and k-Prime Labeling. Journal of Mathematics Research, 3(1).

Vaidya, S. K., & Prajapati, U. M. (2012). Some Switching Invariant Prime Graphs. Open Journal of Discrete Mathematics, 2(1), 17–20. https://doi.org/10.4236/ojdm.2012.21004

Zhang, X., Cancan, M., Nadeem, M. F., & Imran, M. (2020). Edge irregularity strength of certain families of comb graph. Proyecciones, 39(4), 787–797. https://doi.org/10.22199/issn.0717-6279-2020-04-0049.

DOI: http://dx.doi.org/10.26737/var.v5i2.2699

Refbacks

There are currently no refbacks.

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Publisher:

Institute of Managing and Publishing of Scientific Journals, STKIP Singkawang

Address : STKIP Singkawang, Jalan STKIP - Kelurahan Naram, Singkawang, Kalimantan Barat, INDONESIA, 79251
No. Telp. : +62562 420 0344
No. Fax. : +62562 420 0584

VARIABEL

e-ISSN : 2599-3038

p-ISSN : 2599-302X