中文摘要：

假定G是一个非平凡的连通图，对G的边全部着上颜色，相邻的边可以着相同的颜色．用数字表示颜色，并假定c：E（G）→{1，2，…，k，k∈N}是G的一种着色方式．G中的一条道路P称为是一条彩虹路，如果P所经过的边的颜色各不相同．如果图G的任意两点间都有一条彩虹路，则称G是彩虹路连通的．使得图G为彩虹路连通所使用的最少颜色数尼称为G的彩虹路连通数．本文计算了线性多边形链图的彩虹路2一连通度和线性偶数边多边形链图的彩虹路连通数．

英文摘要：

Let G be a nontrivial connected graph on which is defined a coloring c ： E（G） → {1, 2,... , k, k E N） of the edges of G, where adjacent edges may be colored the same. A path P in G is a rainbow path if no two edges of P are colored the same. The graph G is rainbow-connected if G contains a rainbow u - v path for every two vertices u and v of G. The minimum k for which there exists such a k-edge coloring is the rainbow connection number of G. In this paper, we enumerate the rainbow 2-connection number of linear polygon chains and therainbow connection number of linear even-size-polygon chains.