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| 題名: | L(2, 1)-labelings of subdivisions of graphs |
| 作者: | 廖勝強;Chang, Fei-Huang;Chia, Ma-Lian;Kuo, David;Liaw, Sheng-Chyang;Tsai, Meng-Hsuan |
| 貢獻者: | 理學院數學系 |
| 關鍵詞: | [formula omitted]-labeling;[formula omitted]-total labeling;Subdivision |
| 日期: | 2015-02-06 |
| 上傳時間: | 2026-04-23 16:17:01 (UTC+8) |
| 出版者: | Elsevier;Elsevier B.V |
| 摘要: | 摘要： Given a graph G and a function h from E(G) to N, the h-subdivision of G, denoted by G(h), is the graph obtained from G by replacing each edge uv in G with a path P:uxuv1xuv2…xuvn−1v, where n=h(uv). When h(e)=c is a constant for all e∈E(G), we use G(c) to replace G(h). Given a graph G, an L(2,1)-labeling of G is a function f from the vertex set V(G) to the set of all nonnegative integers such that |f(x)−f(y)|≥2 if dG(x,y)=1, and |f(x)−f(y)|≥1 if dG(x,y)=2. A k-L(2,1)-labeling is an L(2,1)-labeling such that no label is greater than k. The L(2,1)-labeling number of G, denoted by λ(G), is the smallest number k such that G has a k-L(2,1)-labeling. We study the L(2,1)-labeling numbers of subdivisions of graphs in this paper. We prove that λ(G(3))=Δ(G)+1 for any graph G with Δ(G)≥4, and show that λ(G(h))=Δ(G)+1 if Δ(G)≥5 and h is a function from E(G) to N so that h(e)≥3 for all e∈E(G), or if Δ(G)≥4 and h is a function from E(G) to N so that h(e)≥4 for all e∈E(G).
出版者： Elsevier B.V
出版日期： 2015-02-06
出處： Discrete mathematics, 2015-02, Vol.338 (2), p.248-255
資源來源： Elsevier ScienceDirect Journals Complete - Autoholdings
版權： 2014 Elsevier B.V.
識別號： ISSN: 0012-365X
識別號： EISSN: 1872-681X
識別號： DOI: 10.1016/j.disc.2014.09.006 |
| 顯示於類別: | [數學系] 期刊論文
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