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Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Open Access Research Article

Some explorations on odd-even graceful labeling of graphs

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pp. 2989–2999Vol. 29Issue 8August 2026DOI: 10.47974/JDMSC-2636 Crossmark XML
Received:
01 Nov 2025
Published Online:
14 Aug 2026
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2636
Pages:
2989–2999

Abstract

Among the vast branches of mathematics, graph theory plays a vital role in applied mathematics and scientific computing. Graph labeling is one of the most prominent areas of graph theory. There exist various types of graphs labeling in the available literature, such as graceful labeling, even graceful labeling, Odd graceful labeling, Odd-Even graceful labeling, and Even-Even graceful labeling etc. The present work deals with a unique kind of graph labeling known as Odd-Even graceful labeling. This paper signifies Odd-Even graceful labeling of some classes of graphs, like coconut tree, comb graph, quadrilateral snake graphs, tristar, and 4-star.

Keywords

Subject Classifications

05C3805C78

References

[1] M. Basher, “Odd-even gracefulness of splitting graph of some standard Graphs,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 25, no. 2, pp. 491-502 (2022).

[2] A. K. Behera, D. Mishra, and P. C. Nayak, “Some new classes of even-even and odd-even graceful graphs,” International Journal of Applied Engineering Research, vol. 10, no. 19, pp. 40171-40176 (2015).

[3] R. Boonklurb, N. Ruamkaew, and S. Singhun, “Directed edge-graceful labeling of digraph consisting of cycles of the same size,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 25, no. 1, pp. 53-72 (2022).

[4] J. A. Gallian, ‘’A Dynamic Survey of Graph Labeling,’’ 25th ed., Dynamic Survey DS6, The Electronic Journal of Combinatorics, (Dec. 2022), doi: 10.37236/11668.

[5] G. Lau, W. C. Shiu, H. Ng, Z. Gao, and K. Schaffer, “On k-super graceful graphs with extremal maximum vertex degree,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 27, no. 6, pp. 1765 (2024).

[6] D. Mishra, A. K. Behera, and P. C. Nayak, “Some Graceful Three Distant Trees By Component Moving Operation,” International Journal of Applied and Computational Mathematics, vol. 3, no. 2, pp. 1195-1202 (2017).

[7] D. E. Nurvazly, S. L. Chasanah, and A. R. Wiranto, “Variations of graceful labeling of subgraph of millipede graph,” AIP Conference Proceedings, vol. 2563, no. 1, pp. 050018 (2022).

[8] A. Rosa, “On certain valuations of the vertices a graph,” International Symposium, Rome, pp. 349-355 (1966).

[9] D. SenthilKumar, R. Anbarasan, and G. Pushparaj, “Edge-odd graceful labeling of cartesian product of two paths,” Journal of Information and Optimization Sciences, vol. 46, no. 3, pp. 591-599 (2025).

[10] V. Senthilkumar and K. Venkatesan, “Odd vertex even edge root square mean labelling graphs,” Journal of Interdisciplinary Mathematics, vol. 27, no. 5, pp. 1001-1008 (2024).

[11] P. Sumathi and S. Tamilselvi, “Modular chromatic number on inflated graphs of some tree graphs,” Journal of Interdisciplinary Mathematics, vol. 27, no. 5, pp. 1039-1052 (2024).

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