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 |
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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: | Journal Item |
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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: | 16 Oct 2017 08:38 |
URI: | http://oro.open.ac.uk/id/eprint/7994 |
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