三条路的笛卡尔乘积图的L(1,2)-标号数

L(1,2)-labeling numbers of Cartesian product of three paths

针对计算机无线网络中的代码分配问题,利用三条路的笛卡尔乘积图刻画三维计算机无线网络,通过研究三条路的笛卡尔乘积图的L(j,k)-标号问题(j<k),获得对应的计算机无线网络的代码分配策略,从而缓解计算无线网络的代码匮乏问题。研究首先给出了各类三条路的笛卡尔乘积图的L(1,2)-标号函数,从而确定了这些图的L(1,2)-标号数的上界;然后,通过研究各类三条路的笛卡尔乘积图的性质以及结构特点,确定这些图的L(1,2)-标号数的下界;最后,得到了任意长度三条路的笛卡尔乘积图的L(1,2)-标号数。

To solve the code assignment problem of the computer wireless network,a three-dimensional wireless network was abstracted as the Cartesian product of three paths. The code assignments of these networks were found and the short of code for the computer wireless network was relieved by studying on the L( j, k)-labeling problem of Carte sian product of three paths(j < k). In this paper,the upper bounds of the L(1,2)-labeling numbers were determined by finding the L(1,2)-labeling functions for the Cartesian product of three paths,and the lower bounds on the L(1,2)-labeling numbers were then determined based on the properties and structures of the Cartesian product of three paths,thus,the L(1,2)-labeling numbers of the Cartesian product of three paths with arbitrary length were determined.