[1] S. Bhoumik and S. Mitra, Graceful labeling of pendant edge extension of complete bipartite graph, Int. J. Math. Anal., 8 no. 58 (2014), 2885-2897. http://dx.doi.org/10.12988/ijma.2014.410334
[2] K. Eshghi, Introduction to Graceful Graphs, Sharif University of Technology, 2002.
[3] J. A. Gallian, A dynamic survey of graph labeling, Electron. J. Comb., 5 Dynamic Survey 6, 43 pp. [4] B. Gayathri and K. Amuthavalli, k-odd mean labeling of prism, Trans. Comb., 4 no. 1 (2015) 49–56. https://doi.org/10.22108/toc.2015.5388
[5] W. Giyarti , K. A. Sugeng and F. Firmansah, The graceful labeling on W Graph, J. Hunan Univ. (Natural Sci.), 48 no. 9 (2021) 11–16. http://jonuns.com/index.php/journal/article/view/743/740
[6] A. Graf, A new graceful labeling for pendant graph, Aequationes Math., 87 no. 1-2 (2014) 135–145. https://doi.org/10.1007/s00010-012-0184-4
[7] V. J. Kaneria, H. P. Chudasama and P. P. Andharia, Absolute mean graceful labeling in path union of various graphs, Math. J. Interdiscip. Sci., 7 no. 1 (2018) 51–56. https://doi.org/10.15415/mjis.2018.71008
[8] V. J. Kaneria and H. M. Makadia, Graceful labeling for swastik graph, Int. J. Math. Appl., 3 no. 3-D (2015) 25–29. https://ijmaa.in/index.php/ijmaa/article/view/473
[9] V. J. Kaneria, H. M. Makadia and R. V. Viradia, Graceful labeling for disconnected grid gelated graphs, Bull. Math. Sci. Appl., 11 (2015) 6–11. https://doi.org/10.18052/www.scipress.com/BMSA.11.6
[10] S. Kosari, X. Qiang, J. Kacprzyk, Q. T. Ain and H. Rashmanlou, A study on topological indices in fuzzy graphs with application in decision making problems, J. Mult.-Valued Logic Soft Comput., 42 no. 5-6 (2024) 567–589.
[11] S. Kosari, X. Shi, J. Kacprzyk, Z. Chen and H. Rashmanlou, A novel description of perfectly regular fuzzy graphs with application in psychological sciences, J. Mult.-Valued Logic Soft Comput., 42 no. 5-6 (2024) 405–424.
[12] J. M. Manulang and K. A. Sugeng, Graceful labeling on torch graph, Indonesian J. Comb., 2 no. 1 (2018) 14–19. http://dx.doi.org/10.19184/ijc.2018.2.1.2
[13] M. Pasaribu, Y. Yundari, and M. Ilyas, Graceful labeling and skolem graceful labeling on the U-star graph and its application in cryptography, Jambura J. Math., 3 no. 2 (2021) 103–114. https://doi:10.34312/jjom.v3i2.9992
[14] V. Rajeswari and K. Thiagarajan, Graceful labeling of wheel graph and middle graph of wheel graph under IBEDE and SIBEDE approach, J. Phys.: Conf. Ser., 1000 no. 1 (2018) 012078. https://dx.doi.org/10.1088/1742-6596/1000/1/012078
[15] Y. Rao, S. Kosari, S. Hameed and Z. Yousaf, Multi-attribute decision-making using q-rung orthopair fuzzy Zagreb index, Artificial Intelligence Review, 58 no. 153 (2025) 1–31.
[16] Renu, Sarita, A. Sehgal and A. Malik, Graceful Labelling of Prime Index Graph of Group Zp × Zpn, Contemp. Math., 4 no. 3 (2023) 612–619. https://doi.org/10.37256/cm.4320232727
[17] A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs (Internat. Sympos., Rome, 1966), Gordon & Breach, New York, 1967 349–355.
[18] A. Sehgal, N. Takshak, P. Maan and A. Malik, Graceful labelling of power graph of group Zk−12 × Z4,
Asian-European J. Math., 15 no. 07 (2022) 2250121. https://doi.org/10.1142/S1793557122501212
[19] C. Velmurugan and V. Ramachandran, M modulo N graceful labeling of path and star, J. Inf. Comput. Sci., 9 no. 12 (2019) 1212–1221. http://mannarcollege.com/SSR/cri%20-%203/3.4.3/papers_m/19-20/40.
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[20] Velmurugan, C., and Ramachandran, V., Algorithm for M modulo N Graceful Labeling of Ladder and Subdivision of Ladder Graphs, Int. J. Math. Combin., 3 (2020) 92–101. https://www.mathcombin.com/upload/file/20201010/1602299495751079482.pdf#page=97
[21] R. J. Wilson, Introduction to Graph Theory, Longman Group Ltd, England, 1998.
[22] R. Yadav, A. Sehgal, S. Sehgal and A. Malik, The chromatic polynomial of grid graph P3 × Pn, J. Appl. Math. and Comp., 70 no 1 (2024) 619–637. https://doi.org/10.1007/s12190-023-01967-4
[23] M. R. Zeen El Deen, Edge even graceful labeling of some graphs, J. Egyptian Math. Soc., 27 no. 1 (2019) 15 pp. https://doi.org/10.1186/s42787-019-0025-x
[24] S. L. Zhou, All trees of diameter four are graceful, Ann. New York Acad. Sci., 576 no. 1 (1989) 700-706. https://doi.org/10.1111/j.1749-6632.1989.tb16451.x