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Preprints, Working Papers, ... Year : 2024

Maximal Line Digraphs

Abstract

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 ≥ 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.
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Dates and versions

hal-04587485 , version 1 (24-05-2024)
hal-04587485 , version 2 (11-06-2024)

Identifiers

  • HAL Id : hal-04587485 , version 2

Cite

Quentin Japhet, Dimitri Watel, Dominique Barth, Marc-Antoine Weisser. Maximal Line Digraphs. 2024. ⟨hal-04587485v2⟩
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