<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-04587485v2</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-23T11:33:44+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Maximal Line Digraphs</title>
            <author role="crp">
              <persName>
                <forename type="first">Quentin</forename>
                <surname>Japhet</surname>
              </persName>
              <email type="md5">c94032140e934e1a0183dbbf21ad8612</email>
              <email type="domain">uvsq.fr</email>
              <idno type="idhal" notation="numeric">1385444</idno>
              <idno type="halauthorid" notation="string">3156635-1385444</idno>
              <affiliation ref="#struct-456060"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Dimitri</forename>
                <surname>Watel</surname>
              </persName>
              <email type="md5">155469e5fb734c11f0e38965783457c2</email>
              <email type="domain">ensiie.fr</email>
              <idno type="idhal" notation="string">dimitri-watel</idno>
              <idno type="idhal" notation="numeric">181821</idno>
              <idno type="halauthorid" notation="string">31534-181821</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-4365-1092</idno>
              <idno type="IDREF">https://www.idref.fr/184214440</idno>
              <affiliation ref="#struct-563936"/>
              <affiliation ref="#struct-638"/>
              <affiliation ref="#struct-1144063"/>
              <affiliation ref="#struct-179741"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Dominique</forename>
                <surname>Barth</surname>
              </persName>
              <email type="md5">9d0441ce0e7a499a175581ddf08bcef2</email>
              <email type="domain">prism.uvsq.fr</email>
              <idno type="idhal" notation="numeric">835234</idno>
              <idno type="halauthorid" notation="string">167222-835234</idno>
              <idno type="IDREF">https://www.idref.fr/078457033</idno>
              <idno type="VIAF">https://viaf.org/viaf/173151486</idno>
              <affiliation ref="#struct-456060"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Marc-Antoine</forename>
                <surname>Weisser</surname>
              </persName>
              <email type="md5">4f889ae91bb3776d33afb3350f795afd</email>
              <email type="domain">supelec.fr</email>
              <idno type="idhal" notation="string">marc-antoine-weisser</idno>
              <idno type="idhal" notation="numeric">14392</idno>
              <idno type="halauthorid" notation="string">12128-14392</idno>
              <idno type="IDREF">https://www.idref.fr/145266397</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-1006-0798</idno>
              <affiliation ref="#struct-1062147"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Quentin</forename>
                <surname>Japhet</surname>
              </persName>
              <email type="md5">af1bd54733491c9bce1b8f7818bc7b83</email>
              <email type="domain">liane.net</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2024-05-24 16:38:43</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2024-06-11 10:57:04</date>
              <date type="whenWritten">2024-05-24</date>
              <date type="whenModified">2026-01-21 03:31:34</date>
              <date type="whenReleased">2024-06-12 09:00:52</date>
              <date type="whenProduced">2024-05-24</date>
              <date type="whenEndEmbargoed">2024-06-11</date>
              <ref type="file" target="https://hal.science/hal-04587485v2/document">
                <date notBefore="2024-06-11"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-04587485v2/file/zqfbqtqwgqcbgrtnqxkktgkhwyzdnsyg.pdf" id="file-4607986-3998866">
                <date notBefore="2024-06-11"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/2406.05141"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="1546441">
                <persName>
                  <forename>Quentin</forename>
                  <surname>Japhet</surname>
                </persName>
                <email type="md5">af1bd54733491c9bce1b8f7818bc7b83</email>
                <email type="domain">liane.net</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04587485</idno>
            <idno type="halUri">https://hal.science/hal-04587485</idno>
            <idno type="halBibtex">japhet:hal-04587485</idno>
            <idno type="halRefHtml">2024</idno>
            <idno type="halRef">2024</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-4607986-3998866"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="TELECOM-SUDPARIS" corresp="INSTITUT-MINES-TELECOM">Télécom SudParis</idno>
            <idno type="stamp" n="UVSQ">Université de Versailles Saint-Quentin-en-Yvelines</idno>
            <idno type="stamp" n="CENTRALESUPELEC">Ecole CentraleSupélec</idno>
            <idno type="stamp" n="DAVID">Données et algorithmes pour une ville intelligente et durable</idno>
            <idno type="stamp" n="UNIV-PARIS-SACLAY">Université Paris-Saclay</idno>
            <idno type="stamp" n="IP_PARIS">Institut Polytechnique de Paris</idno>
            <idno type="stamp" n="INSTITUTS-TELECOM">composantes instituts telecom </idno>
            <idno type="stamp" n="UVSQ-UPSACLAY" corresp="UNIV-PARIS-SACLAY">UVSQ-UPSACLAY</idno>
            <idno type="stamp" n="UNIVERSITE-PARIS-SACLAY" corresp="UNIV-PARIS-SACLAY">Université Paris-Saclay</idno>
            <idno type="stamp" n="LISN">Laboratoire Interdisciplinaire des Sciences du Numérique</idno>
            <idno type="stamp" n="GS-HUMANITIES-HERITAGE">Graduate School Humanités - Sciences du Patrimoine</idno>
            <idno type="stamp" n="GS-COMPUTER-SCIENCE">Graduate School Computer Science</idno>
            <idno type="stamp" n="LISN-GALAC" corresp="LISN">Graphes, Algorithmes et Combinatoire </idno>
            <idno type="stamp" n="HUB-IA">Hub Intelligence Artificielle de CentraleSupélec</idno>
            <idno type="stamp" n="ENSIIE">ENSIIE</idno>
            <idno type="stamp" n="INSTITUT-MINES-TELECOM">Institut Mines Telecom</idno>
            <idno type="stamp" n="PSACLAY-TEST">Université Paris-Saclay - Collection pour tests</idno>
            <idno type="stamp" n="DEPARTEMENT-DE-MATHEMATIQUES">Collection du Département de Mathématiques</idno>
            <idno type="stamp" n="IP-PARIS-DEPARTEMENT-MATHEMATIQUES">Département de Mathèmatiques</idno>
            <idno type="stamp" n="IP-PARIS-MATHEMATIQUES">IP Paris Département de Mathématiques</idno>
            <idno type="stamp" n="IP-PARIS-INFORMATION-COMMUNICATION-ELECTRONIQUE">IP Paris Département d'Information, de Communication et d'Électronique</idno>
            <idno type="stamp" n="IP-PARIS-INFORMATIQUE-DONNEES-ET-IA">IP Paris Département d'Informatique, de Données et d'IA</idno>
            <idno type="stamp" n="SAMOVAR">Services répartis, Architectures, Modélisation, Validation, Administration des Réseaux</idno>
          </seriesStmt>
          <notesStmt/>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Maximal Line Digraphs</title>
                <author role="crp">
                  <persName>
                    <forename type="first">Quentin</forename>
                    <surname>Japhet</surname>
                  </persName>
                  <email type="md5">c94032140e934e1a0183dbbf21ad8612</email>
                  <email type="domain">uvsq.fr</email>
                  <idno type="idhal" notation="numeric">1385444</idno>
                  <idno type="halauthorid" notation="string">3156635-1385444</idno>
                  <affiliation ref="#struct-456060"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Dimitri</forename>
                    <surname>Watel</surname>
                  </persName>
                  <email type="md5">155469e5fb734c11f0e38965783457c2</email>
                  <email type="domain">ensiie.fr</email>
                  <idno type="idhal" notation="string">dimitri-watel</idno>
                  <idno type="idhal" notation="numeric">181821</idno>
                  <idno type="halauthorid" notation="string">31534-181821</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-4365-1092</idno>
                  <idno type="IDREF">https://www.idref.fr/184214440</idno>
                  <affiliation ref="#struct-563936"/>
                  <affiliation ref="#struct-638"/>
                  <affiliation ref="#struct-1144063"/>
                  <affiliation ref="#struct-179741"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Dominique</forename>
                    <surname>Barth</surname>
                  </persName>
                  <email type="md5">9d0441ce0e7a499a175581ddf08bcef2</email>
                  <email type="domain">prism.uvsq.fr</email>
                  <idno type="idhal" notation="numeric">835234</idno>
                  <idno type="halauthorid" notation="string">167222-835234</idno>
                  <idno type="IDREF">https://www.idref.fr/078457033</idno>
                  <idno type="VIAF">https://viaf.org/viaf/173151486</idno>
                  <affiliation ref="#struct-456060"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Marc-Antoine</forename>
                    <surname>Weisser</surname>
                  </persName>
                  <email type="md5">4f889ae91bb3776d33afb3350f795afd</email>
                  <email type="domain">supelec.fr</email>
                  <idno type="idhal" notation="string">marc-antoine-weisser</idno>
                  <idno type="idhal" notation="numeric">14392</idno>
                  <idno type="halauthorid" notation="string">12128-14392</idno>
                  <idno type="IDREF">https://www.idref.fr/145266397</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-1006-0798</idno>
                  <affiliation ref="#struct-1062147"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
              <idno type="arxiv">2406.05141</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Line Digraph</term>
                <term xml:lang="en">Graph theory</term>
                <term xml:lang="en">Combinatorial</term>
                <term xml:lang="en">Linegraph</term>
                <term xml:lang="en">Line Digraph Graph theory Combinatorial Linegraph</term>
              </keywords>
              <classCode scheme="halDomain" n="info.info-cc">Computer Science [cs]/Computational Complexity [cs.CC]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>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.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-456060" status="VALID">
          <idno type="IdRef">19191620X</idno>
          <idno type="RNSR">201622145F</idno>
          <idno type="ROR">https://ror.org/01xta2p78</idno>
          <idno type="Wikidata">Q51785421</idno>
          <orgName>Données et algorithmes pour une ville intelligente et durable - DAVID</orgName>
          <orgName type="acronym">DAVID</orgName>
          <date type="start">2015-07-01</date>
          <desc>
            <address>
              <addrLine>Bâtiment Descartes — Campus des SciencesUniversité de Versailles Saint-Quentin45 avenue des États-Unis78035 Versailles</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.david.uvsq.fr/</ref>
          </desc>
          <listRelation>
            <relation name="UR 7431" active="#struct-81173" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-563936" status="VALID">
          <idno type="IdRef">238327159</idno>
          <idno type="ISNI">0000000502717600</idno>
          <idno type="ROR">https://ror.org/042tfbd02</idno>
          <idno type="Wikidata">Q48759778</idno>
          <orgName>Institut Polytechnique de Paris</orgName>
          <orgName type="acronym">IP Paris</orgName>
          <date type="start">2019-06-02</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91120 Palaiseau Cedex, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ip-paris.fr</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-638" status="VALID">
          <idno type="IdRef">281286515</idno>
          <idno type="ISNI">0000000403830480</idno>
          <idno type="RNSR">200319330C</idno>
          <orgName>Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux</orgName>
          <orgName type="acronym">SAMOVAR</orgName>
          <desc>
            <address>
              <addrLine>Télécom Sudparis, 9 rue Charles Fourier -91011 Evry cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://samovar.telecom-sudparis.eu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-352124" type="direct"/>
            <relation active="#struct-302102" type="indirect"/>
            <relation name="563936" active="#struct-563936" type="indirect"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-1144063" status="VALID">
          <orgName>Statistiques, Optimisation, Probabilités</orgName>
          <orgName type="acronym">SOP - SAMOVAR</orgName>
          <date type="start">2022-10-24</date>
          <desc>
            <address>
              <addrLine>Télécom Sudparis, 9 rue Charles Fourier -91011 Evry-Courcouronnes cedex</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-638" type="direct"/>
            <relation active="#struct-352124" type="indirect"/>
            <relation active="#struct-302102" type="indirect"/>
            <relation name="563936" active="#struct-563936" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-179741" status="VALID">
          <orgName>Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise</orgName>
          <orgName type="acronym">ENSIIE</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ensiie.fr/</ref>
          </desc>
        </org>
        <org type="researchteam" xml:id="struct-1062147" status="VALID">
          <orgName>Graphes, Algorithmes et Combinatoire - LISN</orgName>
          <orgName type="acronym">GALaC</orgName>
          <date type="start">2021-01-01</date>
          <desc>
            <address>
              <addrLine>Université Paris-Saclay, Bâtiment 650, 91190 Gif-sur-Yvette</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-1061259" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-411575" type="indirect"/>
            <relation active="#struct-419361" type="indirect"/>
            <relation name="UMR9015" active="#struct-441569" type="indirect"/>
            <relation active="#struct-1065373" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-81173" status="VALID">
          <idno type="IdRef">03082057X</idno>
          <idno type="ISNI">0000 0001 2323 0229 </idno>
          <idno type="ROR">https://ror.org/03mkjjy25</idno>
          <orgName>Université de Versailles Saint-Quentin-en-Yvelines</orgName>
          <orgName type="acronym">UVSQ</orgName>
          <date type="start">1991-07-22</date>
          <desc>
            <address>
              <addrLine>55 avenue de Paris - 78035 Versailles cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.uvsq.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-352124" status="VALID">
          <idno type="IdRef">162347510</idno>
          <idno type="ISNI">0000000406406351</idno>
          <idno type="ROR">https://ror.org/05xvk4r52</idno>
          <idno type="Wikidata">Q43305</idno>
          <orgName>Télécom SudParis</orgName>
          <orgName type="acronym">TSP</orgName>
          <desc>
            <address>
              <addrLine>9 rue Charles Fourier -91011 Evry Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.telecom-sudparis.eu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-302102" type="direct"/>
            <relation name="563936" active="#struct-563936" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-302102" status="VALID">
          <idno type="IdRef">192427156</idno>
          <idno type="ISNI">000000012202567X</idno>
          <idno type="ROR">https://ror.org/025vp2923</idno>
          <idno type="Wikidata">Q27962533</idno>
          <orgName>Institut Mines-Télécom [Paris]</orgName>
          <orgName type="acronym">IMT</orgName>
          <date type="start">2012-03-01</date>
          <desc>
            <address>
              <addrLine>19 Place Marguerite Perey, 91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.imt.fr/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-1061259" status="VALID">
          <idno type="IdRef">253160316</idno>
          <idno type="RNSR">202123711L</idno>
          <idno type="ROR">https://ror.org/00rd81916</idno>
          <idno type="Wikidata">Q109620676</idno>
          <orgName>Laboratoire Interdisciplinaire des Sciences du Numérique</orgName>
          <orgName type="acronym">LISN</orgName>
          <date type="start">2021-01-01</date>
          <desc>
            <address>
              <addrLine>Campus Universitaire bât 507Rue du Belvédère91405 Orsay cedexet Campus Universitaire bât 6401 rue Raimond Castaing91190 Gif-sur-Yvette</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.lisn.upsaclay.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
            <relation active="#struct-411575" type="direct"/>
            <relation active="#struct-419361" type="direct"/>
            <relation name="UMR9015" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
          <orgName type="acronym">Inria</orgName>
          <desc>
            <address>
              <addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/en/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-411575" status="VALID">
          <idno type="IdRef">184443237</idno>
          <idno type="ROR">https://ror.org/019tcpt25</idno>
          <orgName>CentraleSupélec</orgName>
          <desc>
            <address>
              <addrLine>3, rue Joliot Curie,Plateau de Moulon,91192 GIF-SUR-YVETTE Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.centralesupelec.fr</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-419361" status="VALID">
          <idno type="IdRef">241345251</idno>
          <idno type="ROR">https://ror.org/03xjwb503</idno>
          <orgName>Université Paris-Saclay</orgName>
          <desc>
            <address>
              <addrLine>Bâtiment Bréguet, 3 Rue Joliot Curie 2e ét, 91190 Gif-sur-Yvette</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.universite-paris-saclay.fr/fr</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="department" xml:id="struct-1065373" status="VALID">
          <orgName>Algorithmes, Apprentissage et Calcul</orgName>
          <orgName type="acronym">AAC</orgName>
          <date type="start">2021-01-01</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-1061259" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-411575" type="indirect"/>
            <relation active="#struct-419361" type="indirect"/>
            <relation name="UMR9015" active="#struct-441569" type="indirect"/>
          </listRelation>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>