Brankovic, Ljiljana

Wanless, Ian M

2011-03

<p>This 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 α-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.</p>

Mathematics in Computer Science, 5(1), p. 11-20

1661-8289

1661-8270

https://hdl.handle.net/1959.11/62012

Birkhaeuser Science

Graceful Labelling: State of the Art, Applications and Future Directions

Journal Article

Publication