L(2, 1)-labelings of subdivisions of graphs

Please use this identifier to cite or link to this item: https://ir.lib.ncu.edu.tw/handle/987654321/109231

Title:	L(2, 1)-labelings of subdivisions of graphs
Authors:	廖勝強;Chang, Fei-Huang;Chia, Ma-Lian;Kuo, David;Liaw, Sheng-Chyang;Tsai, Meng-Hsuan
Contributors:	理學院數學系
Keywords:	[formula omitted]-labeling;[formula omitted]-total labeling;Subdivision
Date:	2015-02-06
Issue Date:	2026-04-23 16:17:01 (UTC+8)
Publisher:	Elsevier;Elsevier B.V
Abstract:	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
Appears in Collections:	[Department of Mathematics] journal & Dissertation

Files in This Item:

File	Description	Size	Format
index.html		0Kb	HTML	15	View/Open

社群 sharing

Loading...