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

Title: Graceful labelling: state of the art, applications and future directions
Creator: Brankovic, Ljiljana; Wanless, Ian M.
Relation: Mathematics in Computer Science Vol. 5, Issue 1, p. 11-20
Publisher Link: http://dx.doi.org/10.1007/s11786-011-0073-6
Publisher: Birkhaeuser Verlag AG
Resource Type: journal article
Date: 2011
Description: 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 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.
Subject: graceful labelling; graph labellings; graph decomposition; Oberwolfach problem; Latin squares; near transversal; map colouring; spectral graph theory
Identifier: http://hdl.handle.net/1959.13/1065058
Identifier: uon:17749
Identifier: ISSN:1661-8270
Language: eng
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