Brinkmann, Gunnar and Crevals, Simon and Melot, Hadrien and Rylands, Leanne and Steffen, Eckhard - alpha-Labelings and the Structure of Trees with Nonzero alpha-Deficit

dmtcs:569 - Discrete Mathematics & Theoretical Computer Science, June 9, 2012, Vol. 14 no. 1
alpha-Labelings and the Structure of Trees with Nonzero alpha-Deficit

Authors: Brinkmann, Gunnar and Crevals, Simon and Melot, Hadrien and Rylands, Leanne and Steffen, Eckhard

We present theoretical and computational results on alpha-labelings of trees. The theorems proved in this paper were inspired by the results of a computer investigation of alpha-labelings of all trees with up to 26 vertices, all trees with maximum degree 3 and up to 36 vertices, all trees with maximum degree 4 and up to 32 vertices and all trees with maximum degree 5 and up to 31 vertices. We generalise a criterion for trees to have nonzero alpha-deficit, and prove an unexpected result on the alpha-deficit of trees with a vertex of large degree compared to the order of the tree.


Source : oai:HAL:hal-00990566v1
Volume: Vol. 14 no. 1
Section: Graph Theory
Published on: June 9, 2012
Submitted on: April 4, 2011
Keywords: alpha-labeling,alpha-deficit,Graceful Tree Conjecture,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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