中文摘要：

为图 G 和二积极整数 j 和 k ， m-L ( j ， k ) G 的 -edge-labeling 是到集合的边上的一项任务{ 0 ， 1 ， 2 ，， m }，以便收到标签的邻近的边至少由 j 不同，并且是距离二的边分开收到标签至少由 k 不同。< 潜水艇 class= “ a-plus-plus ” > j， G 的 k -number 是最小的 m 以便 m-L (j， k )-edge-labeling 被 G 承认。在这篇文章， L (1， 2 ) 为六角形的格子，方形的格子和三角形的格子的 -edge-labeling 被学习，并且界限为 < 潜水艇 class= “ a-plus-plus ” > j，这些图的 k -numbers 被获得。

英文摘要：

For a graph G and two positive integers j and k, an m-L（j, k）-edge-labeling of G is an assignment on the edges to the set {0, 1, 2,..., m}, such that adjacent edges which receive labels differ at least by j, and edges which are distance two apart receive labels differ at least by k. The λj,k-number of G is the minimum m such that an m-L（j, k）-edge-labeling is admitted by G. In this article, the L（1, 2）-edge-labeling for the hexagonal lattice, the square lattice and the triangular lattice are studied, and the bounds for λj,k-numbers of these graphs are obtained.