Closed-Form Formulas for Fibonacci Numbers of Broom and Double Star Graphs
Abstract
Let
Keywords
Full Text:
PDFReferences
G. Chitra and V. Mohanapriya, ‘Fibonacci Antimagic Labeling of Some Special Graphs', International Journal of Emerging Technologies and Innovative Research, vol. 5, no. 6, pp. 750-753, 2018, [Online]. Available: https://www.jetir.org/view?paper=JETIR1806796
N. Y. Sari, E. Noviani, and F. Fran, ‘Pelabelan Fibonacci Prima Ke-K Pada Graf H dan Graf Ulat H_n', Jurnal Publikasi Ilmiah Matematika (KUBIK), vol. 8, no. 2, pp. 89-98, 2023, doi: 10.15575/kubik.v8i2.29290.
D. S. Permatasari and P. Agung, ‘Bilangan Fibonacci dalam Perkembangbiakan Lebah Madu', Jurnal Equation: Teori dan Penelitian Pendidikan Matematika, vol. 5, no. 1, pp. 103-115, Mar. 2022, doi: 10.29300/equation.v5i1.5442.
J. R. Chasnov, Fibonacci Numbers and the Golden Ratio. The Hong Kong University of Science and Technology, 2016. [Online]. Available: https://www.math.hkust.edu.hk/~machas/fibonacci.pdf
D. Grinberg, ‘An Introduction to Graph Theory', Jun. 10, 2025, arXiv: arXiv:2308.04512. doi: 10.48550/arXiv.2308.04512.
F. Susanto, R. Simanjuntak, and E. T. Baskoro, ‘Further Results on the Total Vertex Irregularity Strength of Trees', Electronic Journal of Graph Theory and Applications, vol. 13, no. 1, pp. 123-140, Apr. 2025, doi: 10.5614/ejgta.2025.13.1.9.
K. R. Saoub, Graph Theory: An Introduction to Proofs, Algorithms, and Applications, 1st ed. in Textbooks in mathematics. Boca Raton London New York: CRC Press, 2021. doi: 10.1201/9781138361416.
I. Gutman, V. R. Kulli, and I. R. zepovic, ‘Irregularity Sombor Index', Bulletin of the Academy of Sciences and Arts of the Republic of Serbia, Class of Mathematical and Natural Sciences, vol. 156, pp. 31-37, 2023, doi: 10.5281/zenodo.18005956.
V. Zverovich, Modern Applications of Graph Theory, 1st ed. Oxford: Oxford University Press, 2021. doi: 10.1093/oso/9780198856740.001.0001.
G. Ali, M. Bača, M. Lascsáková, A. Semaničová-Feňovčíková, A. ALoqaily, and N. Mlaiki, ‘Modular Total Vertex Irregularity Strength of Graphs', AIMS Mathematics, vol. 8, no. 4, pp. 7662-7671, 2023, doi: 10.3934/math.2023384.
S. D. Pasham, ‘Using Graph Theory to Improve Communication Protocols in AI-Powered IoT Networks', Research and Analysis Journal, vol. 7, no. 02, pp. 01-32, Feb. 2024, doi: 10.18535/raj.v7i02.390.
H. Prodinger and R. F. Tichy, ‘Fibonacci Numbers of Graphs', The Fibonacci Quarterly, vol. 20, no. 1, pp. 16-21, Feb. 1982, doi: 10.1080/00150517.1982.12430021.
Ö. Eğecioğlu and V. Iršič, ‘Fibonacci-Run Graphs I: Basic Properties', Discrete Applied Mathematics, vol. 295, pp. 70-84, May 2021, doi: 10.1016/j.dam.2021.02.025.
G. Perarnau and W. Perkins, ‘Counting Independent Sets in Cubic Graphs of Given Girth', Journal of Combinatorial Theory, Series B, vol. 133, pp. 211-242, Nov. 2018, doi: 10.1016/j.jctb.2018.04.009.
D. S. Taletskii, ‘On The Number of Independent and K-Dominating Sets in Graphs with Average Vertex
Degree at Most K', Sbornik: Mathematics, vol. 214, no. 11, pp. 1627-1650, 2023, doi: 10.4213/sm9870e.
I. Sason, ‘A Generalized Information-Theoretic Approach for Bounding the Number of Independent Sets
in Bipartite Graphs', Entropy, vol. 23, no. 3, p. 270, Feb. 2021, doi: 10.3390/e23030270.
E. Cohen, W. Perkins, M. Sarantis, and P. Tetali, ‘On the Number of Independent Sets in Uniform, Regular, Linear Hypergraphs', European Journal of Combinatorics, vol. 99, p. 103401, Jan. 2022, doi:
1016/j.ejc.2021.103401.
F. Ignatius and S. Kaspar, ‘A New Graph Labeling with Tribonacci, Fibonacci and Triangular Numbers',
Discover Sustainability, vol. 5, no. 1, p. 130, Jun. 2024, doi: 10.1007/s43621-024-00325-z.
O. Sikhwal and A. Rastogi, ‘Domination, Independence and Fibonacci Numbers in Graphs Containing Disjoint Cycles', International Journal of Computational and Applied Mathematics & Computer Science,
vol. 2, pp. 65-68, Sep. 2022, doi: 10.37394/232028.2022.2.12.
K. U. Sreeja, P. B. Vinodkumar, and P. B. Ramkumar, ‘Independence Polynomial and Z Counting
Polynomial of a Fibonacci Tree', Turkic World Mathematical Society Journal of Applied and Engineering
Mathematics, vol. 21, no. 3, pp. 1569-1577, 2022, doi: 10.47748/twmsjaem.2022.21.3.006.
S. Mitra, A. Pritchard, and S. Bhoumik, ‘On Fibonacci Cordial Labeling of Some Planar Graphs', Turkic World Mathematical Society Journal of Applied and Engineering Mathematics, vol. 15, no. 5, pp. 1153-
, 2025, doi: 10.5281/zenodo.18006093.
J. DeMaio and J. Jacobson, ‘Fibonacci Number of the Tadpole Graph', Electronic Journal of Graph
Theory and Applications, vol. 2, no. 2, pp. 129-138, 2014, doi: 10.5614/ejgta.2014.2.2.5.
A. Knopfmacher, R. F. Tichy, S. Wagner, and V. Ziegler, ‘Graphs, Partitions and Fibonacci Numbers', Discrete Applied Mathematics, vol. 155, no. 10, pp. 1175-1187, May 2007, doi:
1016/j.dam.2006.10.010.
L. A. Dosal-Trujillo and H. Galeana-Sánchez, ‘The Fibonacci Numbers of Certain Subgraphs of Circulant Graphs', AKCE International Journal of Graphs and Combinatorics, vol. 12, no. 2-3, pp. 94-103, Nov. 2015, doi: 10.1016/j.akcej.2015.11.002.
L. A. Dosal-Trujillo and H. Galeana-Sánchez, ‘On the Fibonacci Numbers of the Composition of Graphs', Discrete Applied Mathematics, vol. 266, pp. 213-218, Aug. 2019, doi: 10.1016/j.dam.2019.02.047.
J. Seibert and L. Koudela, ‘The Fibonacci Numbers for The Molecular Graphs of Linear Phenylenes',
International Journal of Pure and Apllied Mathematics, vol. 106, no. 1, Feb. 2016, doi:
12732/ijpam.v106i1.25.
M. M. N. Bangkit and B. Rahadjeng, ‘Dekomposisi Graf Bintang, Graf Bintang Ganda, dan Graf Sapu',
MATHunesa: Jurnal Ilmiah Matematika, vol. 10, no. 1, pp. 218-225, Apr. 2022, doi:
26740/mathunesa.v10n1.p218-225.
M. Ghorbani and M. Dehmer, ‘On the Roots of the Modified Orbit Polynomial of a Graph', Symmetry,
vol. 13, no. 6, p. 972, May 2021, doi: 10.3390/sym13060972.
E. Győri, R. Wang, and S. Woolfson, ‘Extremal Problems of Double Stars', Discrete Mathematics &
Theoretical Computer Science, vol. 24, no. 2, p. 8499, Apr. 2023, doi: 10.46298/dmtcs.8499.
N. Kusumastuti, Raventino, and F. Fran, ‘The Diachromatic Number of Double Star Graph', Journal of Physics: Conference Series, vol. 2106, no. 1, p. 012024, Nov. 2021, doi: 10.1088/1742-
/2106/1/012024.
A. Yurttas Gunes, S. Delen, M. Demirci, A. S. Cevik, and I. N. Cangul, ‘Fibonacci Graphs', Symmetry,
vol. 12, no. 9, p. 1383, Aug. 2020, doi: 10.3390/sym12091383.
DOI: http://dx.doi.org/10.30829/zero.v9i3.26839
Refbacks
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Publisher : Department of Mathematics Faculty of Science and Technology Universitas Islam Negeri Sumatera Utara Medan | ||||
| ||||
 |  |  |  |  |