对于一个整数k〉0,图G的一个k-L1,2-标号是一个映射c:V(G)→{0,1,2…k}且满足对任意的u,v∈V(G),若d(uv)=1,则|c(u)-c(v)|≥1且对任意的u,v∈V(G),若存在w∈V(G),使得u,v∈NG(w),则|c(u)-c(v)|≥2.则使得图G有一个k—L1,2标号的最小的正整数k称为图G的邻域限制标号数,记为L1,2(G).本文主要给出了图G的邻域限制标号问题的几个性质.
A k-L1,2-labelling of graph G is defined as a function c:V (G)→{0,1,2.…k} such that|c(u) - c(v)| ≥ 1 when d(uv) = 1 and when |c(u) - c(v)|≥ 2 there is a vertex w such that u,v ∈NG(w). The lablelling numbers with a condition on neighborhood of G, denoted by L1,2 (G) is the smallest number k such that G has a k-L1,2-labelling . In this paper, some properties k-L1,2-labelling of are given.