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

作者：Brinkmann Gunnar^*; Crevals Simon; Melot Hadrien; Rylands Leanne; Steffen Eckhard

来源：Discrete Mathematics and Theoretical Computer Science, 2012, 14(1): 159-174.

• alpha-labeling
• alpha-deficit
• Graceful Tree Conjecture

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.

• 出版日期2012