ON METRIC DIMENSION IN GENERALIZED PARACHUTE GRAPH AND DUTCH WINDMILL GRAPH CORONA NULL GRAPH

Authors

DOI:

https://doi.org/10.25077/jmua.15.4.594-600.2026

Keywords:

Dimensi metrik, dutch windmill graph corona null graph, generalized parachute graph, resolving set

Abstract

This paper discusses the metric dimension of generalized parachute graphs and Dutch windmill graph corona null graphs. The objective of this study is to determine the metric dimension of both graph classes. The method used in this research is a literature study based on related books and journal articles concerning metric dimension. The results show that the metric dimension of generalized parachute graphs and Dutch windmill graph corona null graphs depends on the number of vertices in the constituent graphs.

Downloads

Download data is not yet available.

References

Chartrand, G., Eroh, L., Johnson, M.A., Oellermann, O.R., 2000, Resolvability in graphs and the metric dimension of a graph, Discrete Applied Mathematics, Vol. 105: 99–113

Slater, P.J., 1975, Leaves of trees, Congressus Numerantium, Vol. 14: 549–559

Harary, F., Melter, R.A., 1976, On the metric dimension of a graph, Ars Combinatoria, Vol. 2: 191–195

Javaid, I., Ahmad, S., Azhar, M.N., 2012, On the metric dimension of generalized Petersen graphs, Ars Combinatoria, Vol. 105: 171–182

Singh, P., Sharma, S., Sharma, S.K., Bhat, V.K., 2021, Metric dimension and edge metric dimension of windmill graphs, AIMS Mathematics, Vol. 6: 9138-9153

Silalahi, R., Mulyono, 2023, Metric Dimensions and Partition Dimensions of a Multiple Fan Graph, Formosa Journal of Science and Technology, Vol. 2: 81–88

Buczkowski, P.S., Chartrand, G., Poisson, C., Zhang, P., 2003, On k dimensional graphs and their bases, Periodica Mathematica Hungarica, Vol. 46: 9–15

Wijaya, S.A., Kusmayadi, T.A., 2019, On the metric dimension of amalgama tion of sunflower and lollipop graph and caveman graph, Journal of Physics: Conference Series, Vol. 1306: 012035

Sabila, M., Kusmayadi, T.A., 2019, On the metric dimension of generalized broken fan graph and edge corona product of path with star graph, Journal of Physics: Conference Series, Vol. 1306: 012017

Sari, P.D., Kusmayadi, T.A., 2020, Metric dimension of starbarbell graphs and the results of edge corona operations on cycle and path graphs, Jurnal Matematika, Vol. 10: 32–43

Kusmayadi, T.A., Indriati, D., Budianto, W.T., Martini, T.S., 2025, The local metric dimension of k-multilevel corona of path, complete and cycle graphs, Communications in Science Bulletin, Vol. 70, in press

Garey, M.R., Johnson, D.S., 1979, Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman and Company, New York

Khuller, S., Raghavachari, B., Rosenfeld, A., 1996, Landmarks in graphs, Discrete Applied Mathematics, Vol. 70: 217–229

Manuel, P.D., Abd-El-Barr, M.I., Rajasingh, I., Rajan, B., 2008, An efficient representation of Benes networks and its applications, Journal of Discrete Algorithms, Vol. 6: 11–19

Diaz, J., Pottonen, O., Serna, M., van Leeuwen, E.J., 2012, On the complexity of metric dimension, Lecture Notes in Computer Science, Vol. 7501: 419–430

Khotimah, H., Susanti, Y., 2019, Total edge irregular strength of double fan graphs and related graphs, Jurnal Matematika Thales (JMT), Vol. 1: 1–11

Downloads

Published

22-10-2026

How to Cite

Kusmayadi, T. A., Ramadhan, L. D., & Wahidah, F. Y. S. (2026). ON METRIC DIMENSION IN GENERALIZED PARACHUTE GRAPH AND DUTCH WINDMILL GRAPH CORONA NULL GRAPH. Jurnal Matematika UNAND, 15(4), 594–600. https://doi.org/10.25077/jmua.15.4.594-600.2026

Issue

Vol. 15 No. 4 (2026)

Section

Articles

License

Copyright (c) 2026 Departemen Matematika dan Sains Data FMIPA UNAND

Creative Commons License

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.