有向双环网络的彩虹路连通性

Rainbow Connectivity of Directed Double Loop Networks

设1≤s1<s2<n.有向双环网络G(n;s1,s2)是如下定义的有向图(V(G),E(G)):其结点集是V(G)=Zn={0,1,2,…,n-1},边集是E(G)={i→i+s1(modn),i→i+s2(modn)|i=0,1,2,…,n-1}.给出了有向双环网络G(n;s1,s2)的彩虹路连通的一个边着色方案,并给出了其彩虹路连通数上界,它主要由G(n;s1,s2)所确定的L-形瓦的2个参数表示.

Let 1≤s1s2n.A directed double loop network G（n;s1,s2）is a digraph（V（G）,E（G））,which is defined as follows：its vertex set V（G）=Zn={0,1,2,…,n-1},and its edge set E（G）={i→i＋s1（modn）,i→i＋s2（modn）｜i=0,1,2,…,n-1}.A rainbow-connected edge color scheme for a directed double loop network,G（n;s1,s2）is proposed in this paper.Thus an upper bound of the rainbow connection number for G（n;s1,s2）is obtained and is mainly represented by two parameters of the L-shaped tile that is determined by G（n;s1,s2）.