Modular Irregular Labeling on Firecrackers Graphs
Abstract
Let G= (V, E) be a graph order n and an edge labeling ψ: E→{1,2,…,k}. Edge k labeling ψ is to be modular irregular -k labeling if exist a bijective map σ: V→Zn with σ(x)= ∑yϵv ψ(xy)(mod n). The modular irregularity strength of G (ms(G))is a minimum positive integer k such that G have a modular irregular labeling. If the modular irregularity strength is none, then it is defined ms(G) = ∞. Investigating the firecrackers graph (Fn,2), we find irregularity strength of firecrackers graph s(Fn,2), which is also the lower bound for modular irregularity strength, and then we construct a modular irregular labeling and find modular irregularity strength of firecrackers graph ms(Fn,2). The result shows its irregularity strength and modular irregularity strength are equal.
Downloads
Metrics
References
Baca, M., Kimakova, Z., Lascsakova, M., & Fenovcikova, A. S. (2021). The irregularity and modular irregularity strength of fan graphs. Symmetry 2021, 13, 605.
Baca, M., Muthugurupackiam, K., Kathiresan, K., & Ramya, S. (2020). Modular irregularity strength of graphs. Journal of graph theory and applications, 435-443.
Balakrishnan, R., & Ranganathan, K. (2012). A textbook of Graph Theory. New York: Springer Science+Business Media.
Bondy, J. A., & Murty, U. S. (1976). Graph theory with aplications. New York: Elsevier Science Publishing Co.,Inc.
Chartrand, G., Jacobon, M. S., Lehel, J., Oellermann, o. R., Ruiz, S., & Saba, F. (1988). Irregular Networks.
Chartrand, G., Lesniak, L., & Zhang, P. (2016). Graphs & Diagraphs. Boca Raton: CRC Press.
Hasmawati. (2020). Pengantar dan jenis-jenis Graf. Makassar: UPT Unhas Press.
Marsudi. (2016). TEORI GRAF. Malang: UB Press.
Munir, R. (2010). Matematika Diskrit. Bandung: Inuntukmatika Bandung.
Sugeng, K. A., Barack, Z. Z., Hinding, N., & Simanjuntak, R. (2021). Modular irregular labeling on double-star and friendship graph. Hindawi, ID 4746609.
Sukirman. (2016). Teori Bilangan. Tangerang: Universitas Terbuka.
Tilukay, M. I. (2021). Modular iiregularity strength of triangular book graph. TENSOR, 53-58.
Copyright (c) 2022 Dermawan Lase, Nurdin Hinding, Amir Kamal Amir
This work is licensed under a Creative Commons Attribution 4.0 International License.
In submitting the manuscript to the journal, the authors certify that:
- They are authorized by their co-authors to enter into these arrangements.
- The work described has not been formally published before, except in the form of an abstract or as part of a published lecture, review, thesis, or overlay journal.
- That it is not under consideration for publication elsewhere,
- That its publication has been approved by all the author(s) and by the responsible authorities – tacitly or explicitly – of the institutes where the work has been carried out.
- They secure the right to reproduce any material that has already been published or copyrighted elsewhere.
- They agree to the following license and copyright agreement.
License and Copyright Agreement
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under Creative Commons Attribution License (CC BY 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
