References
[1] Entry A000055, The On-Line Encyclopedia of Integer Sequences, 2024. Available: https://oeis.org/A000055 [2] Entry A337274, The On-Line Encyclopedia of Integer Sequences, 2024. Available: https://oeis.org/A337274 [3] M. M. Al Aziz, M. F. Hossain, T. Faequa, and M. Kaykobad, “Graceful labeling of trees: Methods and applications,” in Proc. 17th Int. Conf. Computer and Information Technology , IEEE, 2014, pp. 92–95. [4] R. Aldred and B. D. McKay, “Graceful and harmonious labellings of trees,” Bull. Inst. Combin. Appl., vol. 23, 1998, pp. 69–72. [5] D. Anick, “Counting graceful labelings of trees: A theoretical and empirical study,” Discrete Applied Mathematics, vol. 198, 2016, pp. 65–81. [6] J.-C. Bermond and D. Sotteau, “Graph decompositions and g-designs,” in Proc. 5th British Combinatorial Conf., Congressus Numerantium 15, Utilitas Mathematica, 1976, pp. 53–72. [7] M. Best, P. van Emde Boas, and L. H. W. Jr., “A sharpened version of the Aanderaa– Rosenberg conjecture,” 1974. [8] L. Brankovic and M. J. Reynolds, “Computer search for graceful-like labelling: A survey,” Electronic Journal of Graph Theory and Applications, vol. 10, 2022. [9] I. Cahit, “On zero-rotatable small graceful trees: Caterpillars,” ScienceDirect Working Paper, 2002. [10] F. Chung and F. Hwang, “Rotatable graceful graphs,” Ars Combinatoria, vol. 11, 1981, pp. 239–250. [11] M. Edwards and L. Howard, “A survey of graceful trees,” Atlantic Electronic Journal of Mathematics, vol. 1, 2006, pp. 5–30. [12] W. Fang, “A computational approach to the graceful tree conjecture,” arXiv:1003.3045, 2010. [13] J. A. Gallian, “A dynamic survey of graph labeling,” Electronic Journal of Combinatorics, vol. DS6, 2018. [14] E. K. Gnang, “A proof of the Kotzig–Ringel–Rosa conjecture,” arXiv:2202.03178, 2022. [15] S. W. Golomb, “How to number a graph,” in Graph Theory and Computing, Elsevier, 1972, pp. 23–37. [16] M. Horton, “Graceful trees: Statistics and algorithms,” Ph.D. dissertation, University of Tasmania, 2003. [17] P. Hrnčiar and A. Haviar, “All trees of diameter five are graceful,” Discrete Mathematics, vol. 233, 2001, pp. 133–150. [18] C. Huang, A. Kotzig, and A. Rosa, “Further results on tree labellings,” Utilitas Mathematica, vol. 21, 1982, pp. 31–48. [19] P. Keevash and K. Staden, “Ringel’s tree packing conjecture in quasirandom graphs,” arXiv:2004.09947, 2020. [20] R. Montgomery, A. Pokrovskiy, and B. Sudakov, “A proof of Ringel’s conjecture,” Geometric and Functional Analysis, vol. 31, 2021, pp. 663–720. [21] G. Ringel, “Problem 25,” in Theory of Graphs and Its Applications (Proc. Int. Symp., Smolenice, 1963), Czech Academy of Sciences, Prague, 1963. 333 [22] E. Robeva, “An extensive survey of graceful trees,” Undergraduate Honors Thesis, Stanford University, 2011. [23] R. I. Rofa, “A graceful algebraic function labelling of rooted symmetric trees,” arXiv:2109.09511, 2021. [24] A. Rosa et al., “On certain valuations of the vertices of a graph,” in Theory of Graphs (Int. Symposium, Rome), 1966, pp. 349–355. [25] H. Sun, X. Zhang, and B. Yao, “Construction of new graphical passwords with graceful- type labellings on trees,” in Proc. 2nd IEEE Int. Conf. Advanced Information Management, Communicates, Electronic and Automation Control , IEEE, 2018, pp. 1491–1494. [26] F. Van Bussel, “0-centred and 0-ubiquitously graceful trees,” Discrete Mathematics, vol. 277, 2004, pp. 193–218. [27] T.-M. Wang, C.-C. Yang, L.-H. Hsu, and E. Cheng, “Infinitely many equivalent versions of the graceful tree conjecture,” Applicable Analysis and Discrete Mathematics, 2015. [28] R. A. Wright, B. Richmond, A. Odlyzko, and B. D. McKay, “Constant time generation of free trees,” SIAM Journal on Computing, vol. 15, 1986, pp. 540–548.