Maximal Line Digraphs
<|reference_start|>Maximal Line Digraphs: A line digraph $L(G) = (A, E)$ is the digraph constructed from the digraph $G = (V, A)$ such that there is an arc $(a,b)$ in $L(G)$ if the terminal node of $a$ in $G$ is the initial node of $b$. The maximum number of arcs in a line digraph with $m$ nodes is $(m/2)^2 + (m/2)$ if $m$ is even, and $((m - 1)/2)^2 + m - 1$ otherwise. For $m \geq 7$, there is only one line digraph with as many arcs if $m$ is even, and if $m$ is odd, there are two line digraphs, each being the transpose of the other.<|reference_end|>
@article{japhet2024maximal,
    title={Maximal Line Digraphs},
    author={Quentin Japhet (DAVID), Dimitri Watel (IP Paris, SAMOVAR, SOP -
  SAMOVAR, ENSIIE), Dominique Barth (DAVID), Marc-Antoine Weisser (GALaC)},
    journal={arXiv preprint arXiv:2406.05141},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.05141},
    primaryClass={cs.DM cs.CC}
}