Graceful Labeling of Posets

Main Article Content

Dr. Ashok Bhavale
Dr. DEEPAK SHELKE*

Abstract

Abstract


The concept of graph labeling was introduced in the mid-1960s by Rosa. In this paper, we introduce a notion of graceful labeling of a finite poset. We obtain graceful labeling of some postes such as a chain, a fence, and a crown. In 2002 Thakare, Pawar, and Waphare introduced the `adjunct' operation of two lattices with respect to an adjunct pair of elements. We obtain the graceful labeling of an adjunct sum of two chains with respect to an adjunct pair (0, 1).


AMS Subject Classification 2020: 06A05, 06A06, 05C78

Downloads

Download data is not yet available.

Article Details

Bhavale, A., & SHELKE*, D. D. (2025). Graceful Labeling of Posets. Annals of Mathematics and Physics, 8(1), 018–028. https://doi.org/10.17352/amp.000142 (Original work published January 31, 2025)
Research Articles

Copyright (c) 2025 Bhavale AN, et al.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Licensing and protecting the author rights is the central aim and core of the publishing business. Peertechz dedicates itself in making it easier for people to share and build upon the work of others while maintaining consistency with the rules of copyright. Peertechz licensing terms are formulated to facilitate reuse of the manuscripts published in journals to take maximum advantage of Open Access publication and for the purpose of disseminating knowledge.

We support 'libre' open access, which defines Open Access in true terms as free of charge online access along with usage rights. The usage rights are granted through the use of specific Creative Commons license.

Peertechz accomplice with- [CC BY 4.0]

Explanation

'CC' stands for Creative Commons license. 'BY' symbolizes that users have provided attribution to the creator that the published manuscripts can be used or shared. This license allows for redistribution, commercial and non-commercial, as long as it is passed along unchanged and in whole, with credit to the author.

Please take in notification that Creative Commons user licenses are non-revocable. We recommend authors to check if their funding body requires a specific license.

With this license, the authors are allowed that after publishing with Peertechz, they can share their research by posting a free draft copy of their article to any repository or website.
'CC BY' license observance:

License Name

Permission to read and download

Permission to display in a repository

Permission to translate

Commercial uses of manuscript

CC BY 4.0

Yes

Yes

Yes

Yes

The authors please note that Creative Commons license is focused on making creative works available for discovery and reuse. Creative Commons licenses provide an alternative to standard copyrights, allowing authors to specify ways that their works can be used without having to grant permission for each individual request. Others who want to reserve all of their rights under copyright law should not use CC licenses.

Ringel G. Theory of graphs and its applications. In: Proceedings of the Symposium Smolenice. 1963.

Rosa A. On certain valuations of the vertices of a graph. In: Theory of Graphs (International Symposium, Rome, July 1966). Gordon and Breach; Dunod; New York, Paris; 1967. Available from: https://www.scirp.org/reference/referencespapers?referenceid=2964508

Gallian JA. A Dynamic Survey of Graph Labeling. The Electronic Journal of Combinatorics. 2022;25:1-623. Available from: https://www.combinatorics.org/files/Surveys/ds6/ds6v25-2022.pdf

Biatch MP, Bagga JS, Arumugam S. A survey and a new class of graceful unicyclic graphs. AKCE International Journal of Graphs and Combinatorics. 2020;17(2):673–8. Available from: https://doi.org/10.1080/09728600.2020.1832853

Sivaraman R. Graceful graphs and its applications. International Journal of Current Research. 2016;8:41062-7. Available from: https://www.journalcra.com/sites/default/files/issue-pdf/18683.pdf

Venkatesh S, Balasubramanian K. Some results on generating graceful trees. International Journal of Engineering and Technology. 2018;7(4):570–2. Available from: https://doi.org/10.14419/ijet.v7i4.10.21283

Ragukumar P, Sethuraman G. Binomial trees are graceful. AKCE International Journal of Graphs and Combinatorics. 2020;17(1):632–6. Available from: https://doi.org/10.1016/j.akcej.2018.06.005

Thakare NK, Pawar MM, Waphare BN. A structure theorem for dismantlable lattices and enumeration. Periodica Mathematica Hungarica. 2002;45(1-2):147-60. Available from: https://doi.org/10.1023/a:1022314517291

Kelly D, Rival I. Crowns, fences, and dismantlable lattices. Can J Math. 1974;27:1257-71.

Grätzer G. General Lattice Theory. 2nd ed. Birkhäuser Verlag; 1998. Available from: http://dx.doi.org/10.1007/978-3-0348-7633-9

Bhawale AN, Waphare BN. Posets dismantlable by doubly irreducibles. Journal of the Indian Math. Soc. 2021;88(1-2):46-59. Available from: https://doi.org/10.18311/jims/2021/26053

West DB. Introduction to Graph Theory. 2nd ed. Pearson Education. 2015.