Super Connectivity of Line Graphs and Digraphs

  title={Super Connectivity of Line Graphs and Digraphs},
  author={Min L{\"u} and Jun-Ming Xu},
The h-super connectivity κh and the h-super edge-connectivity λh are more refined network reliability 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… CONTINUE READING

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Short paths and connectivity in graphs and digraphs

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