his paper takes a close look at graceful labelling and its applications. We pay special attention to the famous Graceful Tree Conjecture, which has attracted a lot of interest and engaged many researchers over the last 40+ years, and yet to this day remains unsolved. We describe applications of graceful and graceful-like labellings of trees to several well known combinatorial problems and we expose yet another one, namely the connection between I?-labelling of paths and near transversals in Latin squares. Finally, we show how spectral graph theory can be used to further the progress on the Graceful Tree Conjecture.
Brankovic, L., & Wanless, I. M. (2011). Graceful labelling: State of the art, applications and future directions. Mathematics in Computer Science, 5(1), 11 - 20. https://doi.org/10.1007/s11786-011-0073-6