HAMILTONIAN CYCLES IN WIJAYA KUSUMA FLOWER GRAPH
DOI:
https://doi.org/10.25077/jmua.14.2.167-177.2025Keywords:
Hamiltonian cycle, wijaya kusuma flower graph, wheel graph.Abstract
In 1856, William Rowan Hamilton introduced the Icosian game. From this game, the concept of a Hamiltonian graph is defined. Hamiltonian graph is a graph that contains the Hamiltonian cycle, which is a cycle that passes through each vertex exactly once. We constructed a new class of graph which is inspired by the Wijaya Kusuma flower. In this article, we study the Hamiltonian properties of the Wijaya Kusuma flower graph. Based on the proof, it is concluded that the Wijaya Kusuma flower graph is a Hamiltonian graph.
Downloads
References
Ascheuer, N., 1996, Hamiltonian path problems in the on-line optimization of flexible manufacturing systems, Dissertation at Zuse Institute Berlin, Berlin, unpublished.
Grebinski, V., Kucherov, G., 1998, Reconstructing a Hamiltonian cycle by querying the graph: Application to DNA physical mapping, Discrete Applied Mathematics, Vol. 88: 147-165.
O’Callaghan, J.F., 1974, Computing the perceptual boundaries of dot patterns, Computer Graphics and Image Processing, Vol. 3: 141-162.
Eppstein, D., 2007, The traveling salesman problem for cubic graphs, Journal of Graph Algorithms and Applications, Vol. 11: 61-81.
Hung, R. W., Yao, C.C., Chan, S.J., 2015, The Hamiltonian properties of su- pergrid graphs, Theoretical Computer Science, Vol. 602: 132-148.
Kamˇcev, N., 2014, Generalised Knight’s tours, Electronic Journal of Combina- torics, Vol. 21: 1-31.
Leite, J. B., Mantovani, J. R. S., 2015, Distribution system state estimation using the Hamiltonian cycle theory, IEEE Transactions on Smart Grid, Vol. 7: 366-375.
Williams,H.,2023,TheMathematicsofMazes,MathematicsTODAY,Vol.59: 212-214.
Chartrand, G., Lesniak, L., Zhang, P., 2011, Graphs & digraphs, 5th, Chapman & Hall, Boca Raton.
Danarto, I., 2012, Sifat Hamiltonian dan Hipohamiltonian pada Graf Petersen Diperumun (GRn,1&GPn,2), Dissertation at University Islam Negeri Maulana Malik Ibrahim, Malang, unpublished.
Adwita, P. N., Gemawati, S., 2024, Hamiltonian and Hypohamiltonian of gen- eralized petersen graph GPn,6, Journal of Mathematical Sciences and Optimiza- tion, Vol. 1: 72-86.
Itai, A., Papadimitriou, C.H., Szwarcfiter, J.L., 1982, Hamilton paths in grid graphs, SIAM Journal on Computing, Vol. 11: 676-686.
Reay, J.R., Zamfirescu, T.,2000, Hamiltonian cycles in T-graphs, Discrete and Computational Geometry, Vol. 24: 497-502.
Hung, R. W., 2016, Hamiltonian cycles in linear-convex supergrid graphs, Dis- crete Applied Mathematics, Vol. 211: 99-112.
Gordon, V. S., Orlovich, Y. L., Werner, F., 2008, Hamiltonian properties of triangular grid graphs, Discrete Mathematics, Vol. 308: 6166-6188.
Jackson, B., 1980, Hamilton cycles in regular 2-connected graphs, Journal of Combinatorial Theory, Vol. 29: 27-46.
Ku ̈hn, D., Osthus, D.,2012, A survey on Hamilton cycles in directed graphs, European Journal of Combinatorics, Vol. 33: 750-766.
Munir, R., 2009, Matematika diskrit, 3th Informatika Bandung, Bandung.
Makalew,R.A.M.,Montolalu,C.E.,Mananohas,M.L.,2020,LintasanHamil
tonian pada Graf 4-Connected, d’Cartesian, Vol. 9: 181-188.
Rahmawati, N., Rahajeng, B., 2014, Dekomposisi graf sikel, graf roda, graf gir dan graf persahabatan, MATHunesa: Jurnal Ilmiah Matematika, Vol. 3: 64-71.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Departemen Matematika dan Sains Data FMIPA UNAND
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
All articles published in Jurnal Matematika UNAND (JMUA) are open access and licensed under the Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0). This license allows published content to be freely accessed, shared, redistributed, and adapted for any purpose, including commercial use, provided that the applicable license conditions are followed.
Copyright Holder
The copyright of articles published in Jurnal Matematika UNAND is held by the Departemen Matematika dan Sains Data, Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA), Universitas Andalas (UNAND), in accordance with the journal's stated copyright policy.
Author Rights
Under the CC BY-SA 4.0 license, authors may share, distribute, and reuse their published articles, subject to the applicable license conditions. These rights include:
-
Self-Archiving: Authors may deposit their published articles in institutional repositories, personal websites, or academic platforms.
-
Reuse: Authors may reuse their published work in subsequent publications, research, teaching materials, or other lawful purposes, provided that appropriate attribution is maintained.
-
Distribution: Authors may share and distribute their published articles without requiring additional permission under the terms of the license.
Creative Commons License (CC BY-SA 4.0)
Under the CC BY-SA 4.0 license, users are free to:
-
Share: Copy and redistribute the material in any medium or format.
-
Adapt: Remix, transform, and build upon the material for any purpose, including commercial purposes.
These permissions are subject to the following conditions:
-
Attribution: Users must give appropriate credit to the original author(s), retain relevant copyright notices, provide a link to the license, and indicate if changes were made. Attribution must not imply endorsement by the author(s), copyright holder, or journal.
-
ShareAlike: If users remix, transform, or build upon the material, they must distribute their contributions under the same CC BY-SA 4.0 license or a compatible license.
-
No Additional Restrictions: Users may not apply legal terms or technological measures that legally restrict others from exercising the rights granted by the license.
For more information about the CC BY-SA 4.0 license, please visit:
https://creativecommons.org/licenses/by-sa/4.0/
Third-Party Content
Third-party materials, including figures, tables, photographs, and illustrations, are covered by the article's CC BY-SA 4.0 license only when their inclusion under that license is authorized.
Materials excluded from the license must be clearly identified with appropriate copyright notices and attribution. Authors are responsible for obtaining any necessary permissions, while users must comply with the applicable licensing terms or permissions when reusing excluded materials.
Copyright and Licensing Information
Copyright and licensing information should be clearly displayed on each published article's landing page and included in the full-text versions (HTML and PDF), where applicable, to ensure transparency regarding copyright ownership and permitted reuse.
