### 抜粋

A (p,q)-total labeling of a graph G is an assignment f from the vertex set V(G) and the edge set E(G) to the set of nonnegative integers such that |f(x)-f(y)| ≥ p if x is a vertex and y is an edge incident to x, and |f(x) - f(y)| ≥ q if x and y are a pair of adjacent vertices or a pair of adjacent edges, for all x and y in V(G) ∪ E(G). A k-(p,q)-total labeling is a (p,q)-total labeling f:V(G) ∪ E(G)→{0,...,k}, and the (p,q)-total labeling problem asks the minimum k, which we denote by λ _{pq}^{T}(G), among all possible assignments. In this paper, we first give new upper and lower bounds on λ_{pq}^{T}(G) for some classes of graphs G, in particular, tight bounds on λ_{pq}^{T}(T) for trees T. We then show that if p ≤ 3q/2, the problem for trees T is linearly solvable, and give a complete characterization of trees achieving λ_{pq}^{T}(T) if in addition Δ ≥ 4 holds, where Δ is the maximum degree of T. It is contrasting to the fact that the L(p,q)-labeling problem, which is a generalization of the (p,q)-total labeling problem, is NP-hard for any two positive integers p and q such that q is not a divisor of p.

元の言語 | 英語 |
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ホスト出版物のタイトル | Algorithms and Computation - 21st International Symposium, ISAAC 2010, Proceedings |

ページ | 49-60 |

ページ数 | 12 |

エディション | PART 2 |

DOI | |

出版物ステータス | 出版済み - 12 1 2010 |

イベント | 21st Annual International Symposium on Algorithms and Computations, ISAAC 2010 - Jeju Island, 大韓民国 継続期間: 12 15 2010 → 12 17 2010 |

### 出版物シリーズ

名前 | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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番号 | PART 2 |

巻 | 6507 LNCS |

ISSN（印刷物） | 0302-9743 |

ISSN（電子版） | 1611-3349 |

### その他

その他 | 21st Annual International Symposium on Algorithms and Computations, ISAAC 2010 |
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国 | 大韓民国 |

市 | Jeju Island |

期間 | 12/15/10 → 12/17/10 |

### フィンガープリント

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### これを引用

*Algorithms and Computation - 21st International Symposium, ISAAC 2010, Proceedings*(PART 2 版, pp. 49-60). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻数 6507 LNCS, 番号 PART 2). https://doi.org/10.1007/978-3-642-17514-5_5