关于两类平面图及相关图的L(2,1)-标号问题  

The L(2,1)-Labeling Problem on Two Classes of Plane Craphs and Related Graph

作　　者：邵振东[1] 刘家壮[1] 

机构地区：[1]山东大学数学所,济南250100

出　　处：《山东大学学报（理学版）》2003年第1期37-40,共4页Journal of Shandong University(Natural Science)

摘　　要：图G的L( 2 ,1) 标号是一个从顶点集V(G)到非负整数集的函数f(x) ,使得若d(x ,y) =1,则 |f(x) -f(y) | 2 ;若d(x ,y) =2 ,则 |f(x) -f(y) | 1 图G的L( 2 ,1)标号数λ(G)是使得G有max{f(v) :v∈V(G) } =k的L( 2 ,1)标号中的最小数k Griggs和Yeh猜想对最大度为Δ的一般图G ,有λ(G) Δ2 证明了对平面三角剖分图、立体四面体剖分图、平面近四边形剖分图 。An L (2,1)labeling of a graph 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 d(x,y)=1 and ｜f(x)-f(y)｜1 if d(x,y)=2. The L(2,1) labeling number λ(G) of G is the smallest number k such that G has an L (2,1)-Labeling with max ｛f(v):v∈V(G)｝=k. Griggs and Yeh conjecture that λ(G) Δ 2 for any simple graph with maximum degree Δ.It is proved that Griggs and Yeh's conjecture is true for any plane triangulation graph,solid tetrahedron subdivision graph,plane near quadrangle subdivision grahp.

关 键 词：L(2 1)标号 T-染色 平面三角剖分图 立体四面体剖分图 平面近四边形剖分图 

分 类 号：O157.5[理学—数学]