一类积图的局部边路替换图的L(2,1)-标号

L(2,1)-total-labeling to Local-edge-path-replacement of Cartesian Product of Two Paths

图(i=0,1,…,n-1)的一个L(2,1)-标号就是从点集到非负整数集的一个函数,且满足任两个相邻顶点标号差至少为2,以及任两个距离为2的点标号不同.图(i=0,1,…,n-1)的一个(2,1)-全标号就是从点集和边集到非负整数集的一个函数且使得:任两个相邻顶点标号差至少为2;任两个相邻边标号标号差也至少为2;以及任两个关联的点和边标号也不同.本文研究路路的积图的局部边路替换图的L(2,1)-标号,基本得到了路路的Cartesian积的局部边路替换图的L(2,1)-标号数.

An L(2,1)-labeling of a graph G is a function from the vertex set to the set of all nonnegative integers such that the difference between labels of the adjacent vertices is at least two,and the labels of the two vertices whose distance is two are different.A(2,1)-total-labeling of a graph G is a function from the vertex set and edge set to the set of all nonnegative integers such that the difference between labels of the adjacent vertices is at least two,the difference between labels of the adjacent edges is at least two and the labels of a vertex and an edge which are incident are different.In this paper,we study the L(2,1)-labeling of the local-edge-path-replacement of the Cartesian product of two paths,and its L(2,1)-labeling number is almost determined.