Inclusive Distance Antimagic Labeling of Shadow Graph of Complete and Circulant Graph
DOI:
https://doi.org/10.25077/jmua.15.1.57-62.2026Keywords:
(a, d)-Inclusive Distance Antimagic Labeling, Inclusive Distance Antimagic Labeling, Shadow GraphAbstract
Consider a graph $G = (V, E)$ with order $n$. Suppose that we have a bijection $f: V(G) \to \{1, 2, ..., n\}$. A graph $G$ is said to admit an inclusive distance antimagic labeling if every pair of distinct vertices has different weights, with a vertex weight is defined by $w(v) = \sum_{u \in N(v)} f(u) + f(v)$. Furthermore, if the vertex weights form an arithmetic progression with the first term $a$ and the common difference $d$, then $G$ is said to admit an $(a,d)$-inclusive distance antimagic labeling. This paper investigates the inclusive distance antimagic labeling of the shadow graph of the complete and circulant graph.
References
[1] Diestel, R., 2017, Graph Theory, 5th, Springer, Berlin, Germany.
[2] Kamatchi, N., Arumugam, S., 2013, Distance antimagic graphs, J. Combin. Math. Combin. Comput. Vol. 84: 61 – 67
[3] Arumugam, S., Kamatchi, N., 2012, On (a, d)-distance antimagic graphs, Australasian Journal of Combinatorics Vol. 54: 279 – 287
[4] Dafik, D., Alfarisi, R., Prihandini, R. M., Adawiyah, R., Agustin, I. H., 2018, Inclusive Distance Antimagic Graphs, AIP Conference Proceedings 2014: 020083
[5] Cichacz, S., Froncek, D., 2016, Distance magic circulant graphs, Discrete Mathematics Vol. 339: 84 – 94
[6] Ngurah, A. A. G., Inayah, N., Musti, M. I. S., 2024, On D-distance (anti)magic labelings of shadow graph of some graphs, Electronic Journal of Graph Theory and Applications Vol. 12(1): 25 – 34
[7] Vilvred, V., 1994, Sigma-labeled graph and Circulant Graphs, Ph.D. Thesis, University of Kerala, Trivandrum, India
[8] Miller, M., Rodger, C., Simanjuntak, R., 2003, Distance magic labelings of graphs, Australas. J. Combin. Vol. 28: 305 – 315
[9] Sugeng, K. A., Froncek, D., Miller, M., Ryan, J., Walker, J., 2009, On distance magic labeling of graphs, J. Combin. Math. Combin. Comput. Vol. 71: 39 – 48
[10] Simanjuntak, R., Wijaya, K., 2013, On Distance Antimagic Graphs, https://arxiv.org/pdf/1312.7405
[11] Patel, S. K., Vasava, J., 2020, Some results on (a, d)-distance antimagic labeling, Proyecciones Journal of Mathematics Vol. 39: 361 – 381
[12] Ngurah, A. A. G., Inayah, N., 2023, On {0, 1}-Distance Labeling of 2-Regular Graphs, AIP Conf. Proc. 2975: 020004
Downloads
Published
Issue
Section
License
Copyright (c) 2026 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 (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
