Cartesian积的局部边-路替换图的L(2,1)-标号

L(2,1)-labelings of the local-edge-path-replacements of Cartesian products

设d为正整数,图G的一个L(d,1)-标号就是从非负整数集到V(G)的一个函数,且使得2个相邻顶点的标号相差至少是d,2个距离为2的顶点的标号相差至少为1.图G的L(d,1)-标号的跨度就是所有L(d,1)-标号的最大值和最小值之差.图G的L(d,1)-标号数是G的所有L(d,1)-标号下跨度的最小值.在已有研究图G的边-路替换图的L(d,1)-标号基础上,研究了Cartesian积的局部边-路替换图的L(2,1)-标号.

For a positive integer d,an L（d,1）-labeling of a graph Gis an assignment of nonnegative integers to the vertices of V（G）such that the difference between labels of adjacent vertices is at least d,and the difference between labels of vertices whose distance are two aparts is at least 1.The span of an L（d,1）-labeling of a graph Gis the difference between the maximum and minimum integers of all labels.The L（d,1）-labeling-number of Gis the minimum span over all L（d,1）-labelings of G.Based on the work of L（d,1）-labels of the edge-path-replacement of agraph G,we study the L（2,1）-labeling of the local-edge-path-replacements of the Cartesian products.