<?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-00307786</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="2026-05-18T03:17:04+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">A Survey of Knödel Graphs</title>
            <author role="aut">
              <persName>
                <forename type="first">Guillaume</forename>
                <surname>Fertin</surname>
              </persName>
              <email type="md5">e617d377105f08911523aec7e7a39202</email>
              <email type="domain">univ-nantes.fr</email>
              <idno type="idhal" notation="string">guillaume-fertin</idno>
              <idno type="idhal" notation="numeric">11485</idno>
              <idno type="halauthorid" notation="string">1943-11485</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-8251-2012</idno>
              <idno type="IDREF">https://www.idref.fr/095050612</idno>
              <affiliation ref="#struct-95421"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">André</forename>
                <surname>Raspaud</surname>
              </persName>
              <idno type="halauthorid">249771-0</idno>
              <affiliation ref="#struct-3102"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Guillaume</forename>
                <surname>Fertin</surname>
              </persName>
              <email type="md5">e617d377105f08911523aec7e7a39202</email>
              <email type="domain">univ-nantes.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2009-09-15 10:19:22</date>
              <date type="whenModified">2025-05-26 14:36:02</date>
              <date type="whenReleased">2009-09-15 10:22:14</date>
              <date type="whenProduced">2004</date>
              <date type="whenEndEmbargoed">2009-09-15</date>
              <ref type="file" target="https://hal.science/hal-00307786v1/document">
                <date notBefore="2009-09-15"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00307786v1/file/SurveyKnodel.pdf" id="file-307786-41046">
                <date notBefore="2009-09-15"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="129207">
                <persName>
                  <forename>Guillaume</forename>
                  <surname>Fertin</surname>
                </persName>
                <email type="md5">e617d377105f08911523aec7e7a39202</email>
                <email type="domain">univ-nantes.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00307786</idno>
            <idno type="halUri">https://hal.science/hal-00307786</idno>
            <idno type="halBibtex">fertin:hal-00307786</idno>
            <idno type="halRefHtml">&lt;i&gt;Discrete Applied Mathematics&lt;/i&gt;, 2004, 137 (2), pp.173-195</idno>
            <idno type="halRef">Discrete Applied Mathematics, 2004, 137 (2), pp.173-195</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-307786-41046"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-NANTES">Université de Nantes</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="ENSEIRB">Ecole Nationale Supérieure d'Electronique, Informatique et Radiocommunications de Bordeaux</idno>
            <idno type="stamp" n="LINA" corresp="UNIV-NANTES">Laboratoire d'Informatique de Nantes Atlantique</idno>
            <idno type="stamp" n="LINA-COMBI" corresp="LINA">LINA - Equipe COMbinatoire et Bio-Informatique</idno>
            <idno type="stamp" n="UNIV-BORDEAUX">Université de Bordeaux</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="LS2N">Laboratoire des Sciences du Numérique de Nantes</idno>
            <idno type="stamp" n="NANTES-UNIVERSITE">Nantes Université</idno>
            <idno type="stamp" n="UNIV-NANTES-AV2022">Université de Nantes</idno>
            <idno type="stamp" n="UNIVERSITE-BORDEAUX">Université de Bordeaux</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">A Survey of Knödel Graphs</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Guillaume</forename>
                    <surname>Fertin</surname>
                  </persName>
                  <email type="md5">e617d377105f08911523aec7e7a39202</email>
                  <email type="domain">univ-nantes.fr</email>
                  <idno type="idhal" notation="string">guillaume-fertin</idno>
                  <idno type="idhal" notation="numeric">11485</idno>
                  <idno type="halauthorid" notation="string">1943-11485</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-8251-2012</idno>
                  <idno type="IDREF">https://www.idref.fr/095050612</idno>
                  <affiliation ref="#struct-95421"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">André</forename>
                    <surname>Raspaud</surname>
                  </persName>
                  <idno type="halauthorid">249771-0</idno>
                  <affiliation ref="#struct-3102"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">12621</idno>
                <idno type="issn">0166-218X</idno>
                <title level="j">Discrete Applied Mathematics</title>
                <imprint>
                  <publisher>Elsevier</publisher>
                  <biblScope unit="volume">137</biblScope>
                  <biblScope unit="issue">2</biblScope>
                  <biblScope unit="pp">173-195</biblScope>
                  <date type="datePub">2004</date>
                </imprint>
              </monogr>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="info.info-oh">Computer Science [cs]/Other [cs.OH]</classCode>
              <classCode scheme="halDomain" n="info.info-dm">Computer Science [cs]/Discrete Mathematics [cs.DM]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>Knödel graphs of even order n and degree 1\leq Delta \leq \lfloor log2(n)\rfloor, W(Delta,n), are graphs which have been introduced some 25 years ago as the topology underlying a time optimal algorithm for gossiping among n nodes (Discrete Math. 13 (1975) 95). However, they have been formally defined only 7 years ago (Networks 38 (2001) 150). Since then, they have been widely studied as interconnection networks, mainly because of their good properties in terms of broadcasting and gossiping (Int. J. Foundations Comput. Sci. 8(2) (1997) 109, Proceedings of the 24th International Workshop on Graph-Theoretic Concepts in Computer Science, Vol. 1517, Smolenice, LNCS, 1998, p.63). In particular, Knödel graphs of order 2k , and of degree k, are among the three most popular families of interconnection networks in the literature, along with the hypercube of dimension k, Hk (Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes, Morgan Kaufman Publisher, Los Altos, CA, 1992), and with the recursive circulant graph G(2k ; 4) introduced by Park and Chwa in 1994 (Proceedings of the International Symposium on Parallel Architectures, Algorithms and Networks, ISPAN'94, Kanazawa, Japan, 1994, p. 73). Indeed, those three families are commonly presented as good topologies for multicomputer networks, and are comparable since they have the same number of nodes and the same degree. In this paper, we first survey the different results that exist concerning Knödel graphs, mostly in terms of broadcasting and gossiping. We complete this survey by a study of graph–theoretical properties of the “general” Knödel graph W(Delta,n), for any even n and 1\leq Delta\leq \lfloor log2(n)\rfloor. Finally, we propose a rather complete study of Knödel graphs W(k,2k) , which allows to compare this topologyto the hypercube of dimension k, Hk , and the recursive circulant graph G(2k ; 4). We also provide a study of the different embeddings that can exist between any two of these topologies.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-95421" status="OLD">
          <orgName>Laboratoire d'Informatique de Nantes Atlantique</orgName>
          <orgName type="acronym">LINA</orgName>
          <date type="end">2016-12-31</date>
          <desc>
            <address>
              <addrLine>LINA - Faculté des Sciences 2 rue de la Houssinière - BP 92208 44322 NANTES CEDEX 3</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.sciences.univ-nantes.fr/lina</ref>
          </desc>
          <listRelation>
            <relation active="#struct-84538" type="direct"/>
            <relation active="#struct-97058" type="direct"/>
            <relation active="#struct-93263" type="indirect"/>
            <relation name="UMR6241" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-3102" status="VALID">
          <idno type="IdRef">155054465</idno>
          <idno type="ISNI">0000000122898198</idno>
          <idno type="RNSR">199511665F</idno>
          <idno type="ROR">https://ror.org/03adqg323</idno>
          <idno type="Wikidata">Q3214395</idno>
          <orgName>Laboratoire Bordelais de Recherche en Informatique</orgName>
          <orgName type="acronym">LaBRI</orgName>
          <date type="start">1988-01-01</date>
          <desc>
            <address>
              <addrLine>Domaine Universitaire 351, cours de la Libération 33405 Talence Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.labri.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-259761" type="direct"/>
            <relation active="#struct-300366" type="direct"/>
            <relation name="UMR5800 / URA1304" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-84538" status="OLD">
          <orgName>Mines Nantes</orgName>
          <orgName type="acronym">Mines Nantes</orgName>
          <date type="start">1991-10-08</date>
          <date type="end">2016-12-31</date>
          <desc>
            <address>
              <addrLine>La Chantrerie - 4, rue Alfred Kastler - BP 20722 - 44307 Nantes cedex 3</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.mines-nantes.fr/</ref>
          </desc>
        </org>
        <org type="regrouplaboratory" xml:id="struct-97058" status="OLD">
          <orgName>Université de Nantes - UFR des Sciences et des Techniques</orgName>
          <orgName type="acronym">UN UFR ST</orgName>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>2, rue de la Houssinière - BP 92208 - 44322 Nantes cedex 3</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.sciences-techniques.univ-nantes.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-93263" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-93263" status="OLD">
          <idno type="IdRef">026403447</idno>
          <idno type="ROR">https://ror.org/03gnr7b55</idno>
          <orgName>Université de Nantes</orgName>
          <orgName type="acronym">UN</orgName>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>1, quai de Tourville - BP 13522 - 44035 Nantes cedex 1</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-nantes.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="institution" xml:id="struct-259761" status="VALID">
          <idno type="IdRef">175206562</idno>
          <idno type="ROR">https://ror.org/057qpr032</idno>
          <orgName>Université de Bordeaux</orgName>
          <orgName type="acronym">UB</orgName>
          <desc>
            <address>
              <addrLine>35, place Pey Berland - 33076 Bordeaux</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.u-bordeaux.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300366" status="VALID">
          <orgName>École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>