Gunnar Brinkmann ; Simon Crevals ; Hadrien Melot ; Leanne Rylands ; Eckhard Steffen - 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-DeficitArticle

Authors: Gunnar Brinkmann 1; Simon Crevals 1; Hadrien Melot 1; Leanne Rylands 2; Eckhard Steffen 3

  • 1 Department of Applied Mathematics and Computer Science [Ghent]
  • 2 School of Computing, Engineering and Mathematics [Sydney]
  • 3 Paderborn Institute for Advanced Studies in Computer Science and Engineering

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.

Volume: Vol. 14 no. 1
Section: Graph Theory
Published on: June 9, 2012
Accepted on: June 9, 2015
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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