Abstract
In this chapter, several characterizations of line digraphs are given: The first involves partitions of the arcs so that certain properties are satisfied. As a side benefit, this provides the basis for an algorithm for constructing a root digraph of a known digraph. A second involves subdigraphs whose presence demands that there be other arcs in the digraph. A third is algebraic in nature in requiring that the adjacency matrix have a certain property. Characterizations of various important families of line digraphs, including oriented graphs and tournaments are also given.
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References
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Beineke, L.W., Bagga, J.S. (2021). Characterizations of Line Digraphs. In: Line Graphs and Line Digraphs. Developments in Mathematics, vol 68. Springer, Cham. https://doi.org/10.1007/978-3-030-81386-4_11
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DOI: https://doi.org/10.1007/978-3-030-81386-4_11
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