一种特殊三维六度环面网络的彩虹连通性

Rainbow Connectivity of Special Three-Dimensional Six-Degree Torus Network

三维以及更高维环面是二维环面的自然扩展,适合构建规模更大、更为复杂的互连网络结构。给出一般图的彩虹连通数是一件困难事情,所以研究一个图的彩虹连通数的上界成为了人们感兴趣的问题。给出了三维六度环面网络H_(n×n×n)(n=4t)的彩虹连通数的上界,对于该网络的研究具有一定的意义。

Three-dimensional and higher dimensional torus are the natural extension of two-dimensional torus,which are suitable for building larger and more complex interconnection network structure.It is difficult to give the rainbow connected number in a general graph,so it has become a problem of interest to study the upper bound of the connected number of a rainbow in a graph.In this paper,the upper bound of the rainbow connection number of three-dimensional six-degree torus networkH_(n×n×n)(n=4t)is given,it is very meaningful to the network research.