### Abstract

In this paper, we prove that the α-labeling number of trees T, T_{α} ≤ ⌈ r / 2 ⌉ n where n = | E (T) | and r is the radius of T. This improves the known result T_{α} ≤ e^{O (sqrt(n log n))} tremendously and this upper bound is very close to the upper bound T_{α} ≤ n conjectured by Snevily. Moreover, we prove that a tree with n edges and radius r decomposes K_{t} for some t ≤ (r + 1) n^{2} + 1.

Original language | English |
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Pages (from-to) | 3290-3296 |

Number of pages | 7 |

Journal | Discrete Mathematics |

Volume | 306 |

Issue number | 24 |

DOIs | |

State | Published - 28 Dec 2006 |

### Keywords

- α-labeling number
- Tree decomposition

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## Cite this

Shiue, C. L., & Fu, H-L. (2006). α-labeling number of trees.

*Discrete Mathematics*,*306*(24), 3290-3296. https://doi.org/10.1016/j.disc.2006.06.016