Maximally connected and superconnected digraphs
نویسندگان
چکیده
A maximally connected digraph is said to be superconnected if every minimum disconnecting set F of vertices is trivial, i.e., it consists of the vertices adjacent to or from a given vertex not belonging to F . In this work, it is shown that a digraph is maximally connected provided that a certain condition on the diameter holds, and superconnected under a more restrictive constraint. These conditions on the diameter are written in terms of the so-called parameter `, with 1 ≤ π ≤ b δ−1 2 c, δ being the minimum degree of the digraph. Analogous statements are presented in terms of edges (maximally edge-connected, edge-superconnected digraphs). Finally, the obtained results are applied to the iterated line digraphs.
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