Grannell, M.J.; Griggs, T.S. and Holroyd, F.C.
(2001).
| DOI (Digital Object Identifier) Link: | https://doi.org/10.1016/S0012-365X(00)00318-6 |
|---|---|
| Google Scholar: | Look up in Google Scholar |
Abstract
A gracious labelling g of a tree is a graceful labelling in which, treating the tree as a bipartite graph, the label of any edge (d,u) (d a 'down' and u an 'up' vertex) is g(u) - g(d). A gracious k-labelling is one such that each residue class modulo k has teh 'correct' numbers of vertex and edge labels -- that is, the numbers that arise by interpreting the labels of a gracious labelling modulo k. In this paper it is shown that every non-null tree has a gracious k-labelling for each k = 2,3,4,5.
| Item Type: | Article |
|---|---|
| ISSN: | 0012-365X |
| Keywords: | trees; graceful labellings; gracious labellings |
| Academic Unit/School: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |
| Item ID: | 7994 |
| Depositing User: | Fred Holroyd |
| Date Deposited: | 12 Jun 2007 |
| Last Modified: | 04 Oct 2016 10:01 |
| URI: | http://oro.open.ac.uk/id/eprint/7994 |
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