The h-super connectivity κh and the h-super edge-connectivity λh are more refined network reliability indices than the conneetivity and the edge-connectivity. This paper shows that for a connected balanced digraph D and its line digraph L, if D is optimally super edge-connected, then κ1（L） = 2λ1 （D）, and that for a connected graph G and its line graph L, if one of κ1 （L） and λ（G） exists, then κ1（L） = λ2（G）. This paper determines that κ1（B（d, n） is equal to 4d- 8 for n = 2 and d ≥ 4, and to 4d-4 for n ≥ 3 and d ≥ 3, and that κ1（K（d, n）） is equal to 4d- 4 for d 〉 2 and n ≥ 2 except K（2, 2）. It then follows that B（d,n） and K（d, n） are both super connected for any d ≥ 2 and n ≥ 1.
n阶连通图G的路由选择R是由连接G的每个有向顶点对的n(n-1)条路组成.R经过G的每个顶点(每条边)的路的最大条数称为G关于R的点转发指数ξ(G,R)(边转发指数π(G,R)).对G的所有路由选择R,ξ(G,R)(π(G,R))的最小值称为G的点转发指数ξ(G)(边转发指数π(G)).对于k正则k连通图G,Fernandez de la Vega和Manoussakis[Discrete Applied Mathematics,1989,23(2) :103-123]证明ξ(G)≤(n-1)·┌(n-k-1)/k┐和π(G)≤n┌(n-k-1)/k┐,并且猜想ξ(G)≤┌(n-k)(n-k-1)/k┐.我们分别改进了ξ(G)≤(n-1) ┌(n-k-1)/k┐-(n-k-1)和π(G)≤n┌(n-k-1)/k┐-(n-k),并且证明了猜想对k=3的情形.
