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| 題名: | The game L (d, 1) -labeling problem of graphs |
| 作者: | 廖勝強;Chia, Ma-Lian;Hsu, Huei-Ni;Kuo, David;Liaw, Sheng-Chyang;Xu, Zi-teng |
| 貢獻者: | 理學院數學系 |
| 關鍵詞: | Complete bipartite graphs;Complete graphs;Game [formula omitted]-labeling |
| 日期: | 2012-10-28 |
| 上傳時間: | 2026-04-23 16:24:28 (UTC+8) |
| 出版者: | Elsevier;Elsevier B.V |
| 摘要: | 摘要： Let G be a graph and let k be a positive integer. Consider the following two-person game which is played on G: Alice and Bob alternate turns. A move consists of selecting an unlabeled vertex v of G and assigning it a number a from {0,1,2,…,k} satisfying the condition that, for all u∈V(G),u is labeled by the number b previously, if d(u,v)=1, then |a−b|≥d, and if d(u,v)=2, then |a−b|≥1. Alice wins if all the vertices of G are successfully labeled. Bob wins if an impasse is reached before all vertices in the graph are labeled. The gameL(d,1)-labeling number of a graph G is the least k for which Alice has a winning strategy. We use λ̃1d(G) to denote the game L(d,1)-labeling number of G in the game Alice plays first, and use λ̃2d(G) to denote the game L(d,1)-labeling number of G in the game Bob plays first. In this paper, we study the game L(d,1)-labeling numbers of graphs. We give formulas for λ̃1d(Kn) and λ̃2d(Kn), and give formulas for λ̃1d(Km,n) for those d with d≥max{m,n}.
出版者： Elsevier B.V
出版日期： 2012-10-28
出處： Discrete mathematics, 2012-10, Vol.312 (20), p.3037-3045
資源來源： Elsevier ScienceDirect Journals Complete
版權： 2012 Elsevier B.V.
識別號： ISSN: 0012-365X
識別號： EISSN: 1872-681X
識別號： DOI: 10.1016/j.disc.2012.07.002 |
| 顯示於類別: | [數學系] 期刊論文
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