Super connectivity of line graphs and digraphs

Abstract The h-super connectivity κh and the h-super edge-connectivity λh are more refined network relia-bility indices than the connectivity 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 λ2(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 tha