ON CONSTRUCTING $H$-IRREGULARITY LABELING WITH MINIMUM LABEL FOR CERTAIN BALLOON GRAPHS

Authors

DOI:

https://doi.org/10.25077/jmua.15.3.346-357.2026

Keywords:

balloon graph, double balloon graph, double balloon ladder graph, total H-irregularity strength

Abstract

If $\varrho$ and $H$ are simple, connected, undirected graphs, and $\varrho$ can be covered by an $H$-covering, then for a positive integer $p$, a total $p$-labeling $\varphi$ on $\varrho$ is considered as a total $H$-irregular $p$-labeling if, for every subgraph $K$ of $\varrho$ that is isomorphic to $H$, the weight of $K$ (the sum of the labels of all vertices and edges of $K$) is a unique number. The smallest integer $p$ for which graph $\varrho$ can be labeled with a total $H$-irregular $p$-labeling is called the total $H$-irregularity strength of graph $G$. This paper presents the exact total $H$-irregularity strength values for some particular graphs including balloon graphs, double balloon graphs, and double balloon ladder graphs.

References

[1] Wilson, R. J., 2010, Introduction to graph theory, Fifth Edition, Pearson

[2] Wallis, W. D., 2007, A beginner's guide to graph theory, Springer Science & Business Media

[3] Gallian, J. A., 2022, A dynamic survey of graph labeling, Electronic Journal of Combinatorics 1

[4] Chartrand, G., Jacobson, M. S., Lehel, J., 1988, Irregular networks. Congr. Numer., Vol. 64: 187 - 192

[5] Ashraf, F., Baca, M., Lascsakova, M., Semanicova-Fenovcikova, A., 2017, On H-irregularity strength of graphs, Discussiones Mathematicae Graph Theory, Vol. 37(4): 1067 - 1078

[6] Agustin, I. H., Dafik, D., Marsidi, M., and Albirri, E. R., 2017, On the total H-irregularity strength of graphs: a new notion, Journal of Physics: Conference Series, Vol. 855: 012004

[7] Nisviasari, R., Dafik, D., Agustin, I. H., 2019, The total H-irregularity strength of triangular ladder and grid graphs, Journal of Physics: Conference Series, Vol. 1465(1): 012026

[8] Hidayatul, M., Dafik, D., Agustin, I. H., Nisviasari, R., Kurniawati, E.Y., 2020, On total H-irregularity strength of graphs, Journal of Physics: Conference Series, Vol. 1465(1): 012020

[9] Suni, D. M. O., Dafik, D., Tirta, I. M., Kristiana, A. I., and Nisviasari, R., 2020, On total H-irregularity strength of diamond ladder, three circular ladder, and prism graphs, Journal of Physics: Conference Series, Vol. 1465(1): 012021

[10] Wahyujati, M. F., Susanti, Y., 2022, Computing the total H-irregularity strength of edge comb product of graphs, Analele Stiintifice ale Universitatii Ovidius Constanta. Seria Matematica, Vol. 31(2): 177 - 189

[11] Shulhany, M. A., et al., 2022, The total H-irregularity strength of some graph classes, AIP Conference Proceedings, Vol. 2468: 070005

[12] Labane, H., Bouchemakh, I., and Semanicova-Fenovcikova, A., 2022, On H-irregularity strength of cycles and diamond graphs Discrete Mathematics, Algorithms and Applications, Vol. 14(5): 2150157

Downloads

Published

31-07-2026

Issue

Vol. 15 No. 3 (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 (CC BY-SA) license. This ensures that the content is freely available to all users and can be shared and adapted, provided appropriate credit is given and any adaptations are distributed under the same license.

Copyright Holder

The copyright of all 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). This applies to all published versions, including the HTML and PDF formats of the articles.

Author Rights

While the Departemen Matematika dan Sains Data FMIPA UNAND holds the copyright for all published content, authors retain important rights under the Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA). This license grants authors and users the following rights:

  • Reuse: Authors can reuse and distribute their work for any lawful purpose, including sharing on personal websites, institutional repositories, or in subsequent publications.
  • Attribution and Adaptation: Authors and others may remix, adapt, and build upon the published work for any purpose, even commercially, as long as proper credit is given to the original authors, and any derivative works are distributed under the same CC BY-SA license.

Creative Commons License (CC BY-SA)

Under the terms of the CC BY-SA 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, even commercially.

However, the following conditions apply:

  • Attribution: Users must give appropriate credit to the original author(s) and Departemen Matematika dan Sains Data FMIPA UNAND, provide a link to the license, and indicate if changes were made. Attribution must not imply endorsement by the author or the journal.
  • ShareAlike: If users remix, transform, or build upon the material, they must distribute their contributions under the same license as the original.

For more information about the CC BY-SA license, please visit the Creative Commons website.

Third-Party Content

If authors include third-party material (such as figures, tables, or images) that is not covered by a Creative Commons license, they must obtain the necessary permissions for reuse and provide proper attribution. Authors are required to ensure that any third-party content complies with open-access licensing requirements or includes permissions for redistribution under similar terms.

Copyright and Licensing Information Display

The copyright and licensing terms will be clearly displayed on each article's landing page, as well as within the full-text versions (HTML and PDF) of all published articles.

No "All Rights Reserved"

As an open-access journal, JMUA does not use "All Rights Reserved" policies. Instead, the CC BY-SA license ensures that the works remain accessible and reusable for a wide audience while still protecting both the authors' and the copyright holder's rights.

Â