Graceful labelling: State of the art, applications and future directions

Ljiljana Brankovic, Ian Murray Wanless

Research output: Contribution to journalArticleResearchpeer-review

8 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)11 - 20
Number of pages10
JournalMathematics in Computer Science
Issue number1
Publication statusPublished - 2011

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