Fibonacci Prime Labelling on the Class of Flower Graphs

Desi Rahmadani; Afie Ahmadani; Tjang Daniel Chandra; Mochammad Hafiizh

doi:10.20956/j.v22i1.45070

Authors

Desi Rahmadani Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Malang
Afie Ahmadani Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Malang
Tjang Daniel Chandra Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Malang
Mochammad Hafiizh Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Malang

DOI:

https://doi.org/10.20956/j.v22i1.45070

Keywords:

graph labeling, Fibonacci prime labeling, flower graph

Abstract

Graph labeling is one of the significant topics in graph theory. One of its interesting variants is Fibonacci prime labeling, a special type of labeling that assigns Fibonacci numbers as vertex labels while satisfying certain conditions. A graph labeling is an assignment of labels (elements of some set) to elements of a graph, usually the vertices or the edges (or both) of the graph. Several previous studies have shown that some classes of graphs, such as cycle graphs, fan graphs, and umbrella graphs, satisfy the criteria for Fibonacci prime labeling. Moreover, previous research has proven that flower graphs and double flower graphs admit prime labeling. Motivated by these findings, this study aims to explore whether these two classes of graphs also admit Fibonacci prime labeling. This exploration seeks to identify a potential relationship between prime labeling and Fibonacci prime labeling in these graph classes. This research focuses on graphs with an even number of vertices. The methods used include literature review and mathematical proof. The novelty of this study lies in extending the results of prime labeling to Fibonacci prime labeling for flower and double flower graphs. The results show that both graph classes with an even number of vertices belong to the class of graphs that admit Fibonacci prime labeling.

References

[1] Ashokkumar, S., & Maragathavalli, S. 2015. Prime Labelling of Some Special Graphs. IOSR Journal of Mathematics (IOSR-JM), 11(1), 51–58.

[2] Burton, D. M. 2011. Elementary number theory (7. ed). McGraw-Hill. www.rnhhe.com

[3] Chandrakala, S., & Sekar, D. C. 2018. Fibonacci Prime Labeling of Cycle Related Graphs.

International Journal for Research in Engineering Application & Management (IJREAM), 04(03), 805–807.

[4] Chartrand, G., Egan, C., & Zhang, P. 2019. How to Label a Graph. Springer International Publishing.

[5] Gallian, J. A. 2022. A Dynamic Survey of Graph Labeling. The Electronic Journal of Combinatorics, 1000, DS6: Dec 2.

[6] Grimaldi, R. 2012. Fibonacci and Catalan Numbers: An Introduction (illustrated ed.). John Wiley & Sons.

[7] Gross, J. L., & Yellen, J. 2004. Handbook of Graph Theory. CRC Press LLC.

[8] Hartsfield, N., & Ringel, G. 1990. Pearls in Graph Theory—A Comprehensive Introduction. Academic Press.

[9] Jeshinta, J. J, & Stanley, E. H. 2013. Graceful labeling of bow graphs and shell flower graphs. International Journal of Computing Algorithm, 02(01), 62–64.

[10] Jenifer, J., & Subbulakshmi, M. 2021. Fibonacci Prime Labeling of Snake Graph. South East Asian Journal of Mathematics and Mathematical Sciences, 17, 51–58.

[11] Levit, V. E., & Mandrescu, E. 2005. The independence polynomial of a graph—A survey. arXiv preprint [arXiv:0904.4819]. https://arxiv.org/abs/0904.4819.

[12] Nair, M., S., & Suresh, J. S. 2023. Fibonacci Vertex Prime Labelings of Some Graphs. Mapana – Journal of Sciences, 22(1), 179–185.

[13] Parameswari, R., Pritha, K. S, & Rajeswari, R. 2021. Integer Cordial and Face Integer Cordial Labeling of Some Flower Graphs. Journal of Physics: Conference Series, 1770(1), 012079.

[14] Periasamy, K., Venugopal, K., & Raj, P. L. R. 2022. K-th Fibonacci Prime Labeling of Graphs. International Journal of Mathematics Trends and Technology, 68(5), 61–67.

[15] Rahmadani, D., Aldiansyah, A., Pratiwi, D., Yunus, M., & Kusumasari, V. 2025. Prime Labeling ofn Amalgamation of Flower Graphs. Barekeng: Journal of Mathematics and its Applocations, Accepted.

[16] Rosen, K. H. (2019). Discrete mathematics and its applications (8th ed). McGraw-Hill education. mheducation.com/highered

[17] Rosen, K.H. 2011. Elementary Number Theory and Its Applications. Addison-Wesley.

[18] Sari, N. Y., Noviani, E., & Fran, F. 2023. Pelabelan Fibonacci Prima ke-k pada Graf H dan Graf Ulat H_n. Jurnal Publikasi Ilmiah Matematika, 8(2), 89–98.

[19] Sekar, D. C., & Chandrakala, S. 2018. Fibonacci Prime Labeling of Graphs. International Journal of Creative Research Thoughts, 995–1001.