论文信息 - α-Labelings and the Structure of Trees with Nonzero α-Deficit

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

We present theoretical and computational results on α -labelings of trees. The theorems proved in this paper were inspired by the results of a computer investigation of α -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 α -deficit, and prove an unexpected result on the α -deficit of trees with a vertex of large degree compared to the order of the tree.

[1] Pavel Hrnciar,et al. All trees of diameter five are graceful , 2001, Discret. Math..

[2] Brendan D. McKay,et al. Isomorph-Free Exhaustive Generation , 1998, J. Algorithms.

[3] Shizhen Zhao,et al. All Trees of Diameter Four Are Graceful , 1989 .

[4] Jozef Širáň,et al. Bipartite labeling of trees with maximum degree three , 1999 .

[5] Frank Van Bussel. Towards the graceful tree conjecture , 2000 .

[6] Joseph A. Gallian,et al. A Dynamic Survey of Graph Labeling , 2009, The Electronic Journal of Combinatorics.

[7] Robert E. L. Aldred,et al. Graceful and harmonious labellings of trees , 1998 .

[8] Ljiljana Brankovic,et al. Towards the Graceful Tree Conjecture: A Survey , 2004 .

[9] Brendan D. McKay,et al. Practical graph isomorphism, II , 2013, J. Symb. Comput..

[10] Alexander Rosa,et al. Bipartite labelings of trees and the gracesize , 1995, J. Graph Theory.

[11] J. Bermond,et al. Graph decompositions and G-designs , 1976 .

[12] A. Rosa,et al. Labellings of trees with maximum degree three - an improved bound , 2005 .

[13] Gabriel Nivasch,et al. Nonattacking Queens on a Triangle , 2005 .

[14] Frank Ruskey,et al. The advantages of forward thinking in generating rooted and free trees , 1999, SODA '99.