δ and prime-labelling of a tree from caterpillars

Sethukkarasi, A.; Vidyanandini, S.; Nayak, Soumya Ranjan

doi:10.47974/JDMSC-2090

Open Access Research Article

δ and prime-labelling of a tree from caterpillars

A. Sethukkarasisa0421@srmist.edu.inDepartment of Mathematics SRM Institute of Science and Technology College of Engineering and TechnologyKattankulathur, Tamil Nadu, 603202, IndiaView full profile → , ^*S. VidyanandiniCorresponding authorvidyanas@srmist.edu.inDepartment of Mathematics SRM Institute of Science and Technology College of Engineering and TechnologyDepartment of Mathematics SRM Institute of Science and Technology College of Engineering and Technology KattankulathurChengalpattu, Tamil Nadu, 603203, IndiaView full profile → , Soumya Ranjan Nayaknayak.soumya17@gmail.comSchool of Computer Engineering Kalinga Institute of Industrial Technology (Deemed to be University)Bhubaneswar, Odisha, 751024, IndiaView full profile →

* Corresponding author · click or hover a name for details

pp. 2179–2190Vol. 27Issue 7October 2024DOI: 10.47974/JDMSC-2090 Crossmark XML

Received:: 06 Mar 2024
Published Online:: 15 Oct 2024
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2090
Pages:: 2179–2190

Abstract

This paper explores δ-labelling and prime labelling for trees derived from caterpillar structures. In δ-labelling, vertex labels induce injective edge labels, while prime labelling ensures adjacent vertices have a greatest common divisor of one. An algorithm for efficiently labelling caterpillar trees using both methods is introduced. These labelling techniques have practical applications in network security and cryptography, providing new strategies to strengthen the security and robustness of communication networks and cryptographic systems.

Keywords

δ - Labelling Prime labelling Tree and caterpillars

Subject Classifications

Primary 05C78Secondary 05C69

References

[1] A. Rosa. “On certain valuations of the vertices of a graph”, in Theory of Graphs. Internat. Symposium, Rome, Gordon and Breach, N. Y. and Dunod Paris, pp. 349 – 355 (1967).
[2] D.B. West, “Introduction to Graph Theory”, second ed., Prentice-Hall, Englewood cliffs, NJ (2001).
[3] K.M. Koh, D. G. Rogers and T. Tan. “On graceful trees”, Nanta Math. Vol. 10(2), pp. 27 – 31 (1997).
[4] P. Hrnciar and Alfonz Haviar. “All trees of diameter five are graceful”, Disc. Math, Vol. 233 (1 − 3), pp. 133-150 (2001).
[5] R.E.L. Aldred and B.D. McKay. “Graceful and harmonious labelings of trees”, Bull. Inst. Combin. Appl, Vol. 23, pp. 69-72, (1998).
[6] M. M. Al Aziz, M. F. Hossain, T. Faequa and M. Kaykobad, “Graceful labeling of trees: Methods and applications”, 2014 17th International Conference on Computer and Information Technology (ICCIT), Dhaka, Bangladesh, pp. 92-95, (2014).
[7] W. Fang. “A computational approach to the graceful tree conjecture” Accessed July 31(2011). http://arxiv.org/abs/1003.3045.
[8] J. A Gallian, “A Dynamic Survey of Graph Labeling”, The Electronic Journal of Combinatorics, Vol. 15 (2008).
[9] S. W Golomb, “How to number a graph”, in Graph Theory and Computing, R. C. Read,ed., Academic Press, New York, pp. 23-37 (1972).
[10] M Horton, “Graceful Trees: Statistics and Algorithms”, Ph. D. Thesis, University of Tasmania (2003).
[11] G. Sethuraman, V. Murugan, “Decomposition of Complete Graphs into Arbitrary Trees” Graphs and Combinatorics 37, 1191-1203 (2021).
[12] N. Parvathi and S. Vidyanandini. “Graceful Labeling of a Tree from Caterpillars”, Journal of Information and Optimization Sciences. 35:4, pp. 387-393(2014).
[13] A. Sethukkarasi , S Vidyanandini & Nayak, Soumya Ranjan (2024) “Local antimagic vertex coloring of a Myceilski of graphs”. Journal of Discrete Mathematical Sciences and Cryptography, 27:4, 1389–1401(2024).
[14] A. Sethukkarasi and S. Vidyanandini, “Graph Composite Labeling techniques and Practical Applications”, 2024 International Conference on Emerging Systems and Intelligent Computing (ESIC), Bhubaneswar, India, pp. 526-532 (2024).
[15] J Maowa. “Study on graceful labeling of trees”. M. Sc. Thesis, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh (2016).

Views: 158Downloads: 7Citations: 0