Abstract
Unlike iterated line graphs, where, with the exception of paths, cycles, and the claw, the number of vertices increases monotonically after possibly one step, more interesting things can happen, one being that connectedness is not necessarily preserved. Another instance is that a digraph can be isomorphic to its second iterated line digraph but not to its first. In more general terms, there are digraphs for which, after a while, the sequence of iterated line digraphs becomes periodic. This is just one of the interesting features of this chapter. In addition, second-order line digraphs are characterized, a result that is quite complicated. This is followed by its application to some special classes of digraphs.
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