The (p,q)-total labeling problem for trees

Toru Hasunuma, Toshimasa Ishii, Hirotaka Ono, Yushi Uno

研究成果: 書籍/レポート タイプへの寄稿会議への寄与


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 pqT(G), among all possible assignments. In this paper, we first give new upper and lower bounds on λpqT(G) for some classes of graphs G, in particular, tight bounds on λpqT(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 λpqT(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.

ホスト出版物のタイトルAlgorithms and Computation - 21st International Symposium, ISAAC 2010, Proceedings
出版ステータス出版済み - 2010
イベント21st Annual International Symposium on Algorithms and Computations, ISAAC 2010 - Jeju Island, 韓国
継続期間: 12月 15 201012月 17 2010


名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
番号PART 2
6507 LNCS


その他21st Annual International Symposium on Algorithms and Computations, ISAAC 2010
CityJeju Island

!!!All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)


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