alpha-Labelings and the Structure of Trees with Nonzero alpha-Deficit

Abstract : 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.
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Discrete Mathematics and Theoretical Computer Science, DMTCS, 2012, Vol. 14 no. 1 (1), pp.159-174
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Gunnar Brinkmann, Simon Crevals, Hadrien Melot, Leanne Rylands, Eckhard Steffen. alpha-Labelings and the Structure of Trees with Nonzero alpha-Deficit. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2012, Vol. 14 no. 1 (1), pp.159-174. 〈hal-00990566〉

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