Serveur d'exploration sur la recherche en informatique en Lorraine

Attention, ce site est en cours de développement !
Attention, site généré par des moyens informatiques à partir de corpus bruts.
Les informations ne sont donc pas validées.

Recognizing Knödel graphs

Identifieur interne : 005755 ( Hal/Checkpoint ); précédent : 005754; suivant : 005756

Recognizing Knödel graphs

Auteurs : Johanne Cohen [France] ; Pierre Fraigniaud ; Cyril Gavoille

Source :

RBID : Hal:inria-00100969

English descriptors

Abstract

Given a circulant digraph H=(V,A) of order n and of generators \gamma_0,...,\gamma_k , 0\leq \gamma_i \leq n-1 , i=0,...,k, the bipartite incident-graph of H is a bipartite graph G=(V_1,V_2,E) of order 2n where V_1=V_2=V, and, for any , and any , \{x_1,x_2\}\in E \Leftrightarrow (x_1,x_2)\in A \Leftrightarrow \exists i \in \{0,\dots,k\} \mid x_2 = x_1 + \gamma_i \pmod{n} . Knödel graphs and Fibonacci graphs are two types of such graphs. They correspond to \gamma_i=2^i-1, and \gamma_i=F(i+1)-1 , respectively. Both graphs have been extensively studied for the purpose of fast communications in networks, and they have deserved a lot of attention in this context. In this paper, we show that there exists a polynomial-time algorithm to recognize Knödel graphs, and that the same technique applies to Fibonacci graphs. The algorithm is based on a characterization of the cycles of length six in these graphs (bipartite incident-graphs of circulant digraphs always have cycles of length six). A consequence of our result is that none of the Knödel graphs are edge-transitive, apart those of 2^k-2 vertices. An open problem that arises in this field is to know whether a polynomial-time algorithm exists for any infinite family of bipartite incident-graphs of circulant digraphs indexed by their number of vertices.

Url:

Links toward previous steps (curation, corpus...)


Links to Exploration step

Hal:inria-00100969

Le document en format XML

<record>
<TEI>
<teiHeader>
<fileDesc>
<titleStmt>
<title xml:lang="it">Recognizing Knödel graphs</title>
<author>
<name sortKey="Cohen, Johanne" sort="Cohen, Johanne" uniqKey="Cohen J" first="Johanne" last="Cohen">Johanne Cohen</name>
<affiliation wicri:level="1">
<hal:affiliation type="researchteam" xml:id="struct-2363" status="OLD">
<idno type="RNSR">199621458W</idno>
<orgName>Software Tools for Telecommunications and Distributed Systems</orgName>
<orgName type="acronym">RESEDAS</orgName>
<desc>
<address>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/resedas</ref>
</desc>
<listRelation>
<relation active="#struct-160" type="direct"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-300291" type="indirect"></relation>
<relation active="#struct-300292" type="indirect"></relation>
<relation active="#struct-300293" type="indirect"></relation>
<relation active="#struct-2496" type="direct"></relation>
</listRelation>
<tutelles>
<tutelle active="#struct-160" type="direct">
<org type="laboratory" xml:id="struct-160" status="OLD">
<orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
<orgName type="acronym">LORIA</orgName>
<desc>
<address>
<addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr</ref>
</desc>
<listRelation>
<relation name="UMR7503" active="#struct-441569" type="direct"></relation>
<relation active="#struct-300009" type="direct"></relation>
<relation active="#struct-300291" type="direct"></relation>
<relation active="#struct-300292" type="direct"></relation>
<relation active="#struct-300293" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle name="UMR7503" active="#struct-441569" type="indirect">
<org type="institution" xml:id="struct-441569" status="VALID">
<idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</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"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect">
<org type="institution" xml:id="struct-300009" status="VALID">
<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"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300291" type="indirect">
<org type="institution" xml:id="struct-300291" status="OLD">
<orgName>Université Henri Poincaré - Nancy 1</orgName>
<orgName type="acronym">UHP</orgName>
<date type="end">2011-12-31</date>
<desc>
<address>
<addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine>
<country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300292" type="indirect">
<org type="institution" xml:id="struct-300292" status="OLD">
<orgName>Université Nancy 2</orgName>
<date type="end">2011-12-31</date>
<desc>
<address>
<addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300293" type="indirect">
<org type="institution" xml:id="struct-300293" status="OLD">
<orgName>Institut National Polytechnique de Lorraine</orgName>
<orgName type="acronym">INPL</orgName>
<date type="end">2011-12-31</date>
<desc>
<address>
<country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle active="#struct-2496" type="direct">
<org type="laboratory" xml:id="struct-2496" status="OLD">
<orgName>INRIA Lorraine</orgName>
<desc>
<address>
<addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/centre-de-recherche-inria/nancy-grand-est</ref>
</desc>
<listRelation>
<relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName>
<settlement type="city">Nancy</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université Nancy 2</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName>
<placeName>
<settlement type="city">Nancy</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Institut national polytechnique de Lorraine</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName>
</affiliation>
</author>
<author>
<name sortKey="Fraigniaud, Pierre" sort="Fraigniaud, Pierre" uniqKey="Fraigniaud P" first="Pierre" last="Fraigniaud">Pierre Fraigniaud</name>
</author>
<author>
<name sortKey="Gavoille, Cyril" sort="Gavoille, Cyril" uniqKey="Gavoille C" first="Cyril" last="Gavoille">Cyril Gavoille</name>
</author>
</titleStmt>
<publicationStmt>
<idno type="wicri:source">HAL</idno>
<idno type="RBID">Hal:inria-00100969</idno>
<idno type="halId">inria-00100969</idno>
<idno type="halUri">https://hal.inria.fr/inria-00100969</idno>
<idno type="url">https://hal.inria.fr/inria-00100969</idno>
<date when="2002">2002</date>
<idno type="wicri:Area/Hal/Corpus">006B80</idno>
<idno type="wicri:Area/Hal/Curation">006B80</idno>
<idno type="wicri:Area/Hal/Checkpoint">005755</idno>
<idno type="wicri:explorRef" wicri:stream="Hal" wicri:step="Checkpoint">005755</idno>
</publicationStmt>
<sourceDesc>
<biblStruct>
<analytic>
<title xml:lang="it">Recognizing Knödel graphs</title>
<author>
<name sortKey="Cohen, Johanne" sort="Cohen, Johanne" uniqKey="Cohen J" first="Johanne" last="Cohen">Johanne Cohen</name>
<affiliation wicri:level="1">
<hal:affiliation type="researchteam" xml:id="struct-2363" status="OLD">
<idno type="RNSR">199621458W</idno>
<orgName>Software Tools for Telecommunications and Distributed Systems</orgName>
<orgName type="acronym">RESEDAS</orgName>
<desc>
<address>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/resedas</ref>
</desc>
<listRelation>
<relation active="#struct-160" type="direct"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-300291" type="indirect"></relation>
<relation active="#struct-300292" type="indirect"></relation>
<relation active="#struct-300293" type="indirect"></relation>
<relation active="#struct-2496" type="direct"></relation>
</listRelation>
<tutelles>
<tutelle active="#struct-160" type="direct">
<org type="laboratory" xml:id="struct-160" status="OLD">
<orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
<orgName type="acronym">LORIA</orgName>
<desc>
<address>
<addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr</ref>
</desc>
<listRelation>
<relation name="UMR7503" active="#struct-441569" type="direct"></relation>
<relation active="#struct-300009" type="direct"></relation>
<relation active="#struct-300291" type="direct"></relation>
<relation active="#struct-300292" type="direct"></relation>
<relation active="#struct-300293" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle name="UMR7503" active="#struct-441569" type="indirect">
<org type="institution" xml:id="struct-441569" status="VALID">
<idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</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"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect">
<org type="institution" xml:id="struct-300009" status="VALID">
<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"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300291" type="indirect">
<org type="institution" xml:id="struct-300291" status="OLD">
<orgName>Université Henri Poincaré - Nancy 1</orgName>
<orgName type="acronym">UHP</orgName>
<date type="end">2011-12-31</date>
<desc>
<address>
<addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine>
<country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300292" type="indirect">
<org type="institution" xml:id="struct-300292" status="OLD">
<orgName>Université Nancy 2</orgName>
<date type="end">2011-12-31</date>
<desc>
<address>
<addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300293" type="indirect">
<org type="institution" xml:id="struct-300293" status="OLD">
<orgName>Institut National Polytechnique de Lorraine</orgName>
<orgName type="acronym">INPL</orgName>
<date type="end">2011-12-31</date>
<desc>
<address>
<country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle active="#struct-2496" type="direct">
<org type="laboratory" xml:id="struct-2496" status="OLD">
<orgName>INRIA Lorraine</orgName>
<desc>
<address>
<addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/centre-de-recherche-inria/nancy-grand-est</ref>
</desc>
<listRelation>
<relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName>
<settlement type="city">Nancy</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université Nancy 2</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName>
<placeName>
<settlement type="city">Nancy</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Institut national polytechnique de Lorraine</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName>
</affiliation>
</author>
<author>
<name sortKey="Fraigniaud, Pierre" sort="Fraigniaud, Pierre" uniqKey="Fraigniaud P" first="Pierre" last="Fraigniaud">Pierre Fraigniaud</name>
</author>
<author>
<name sortKey="Gavoille, Cyril" sort="Gavoille, Cyril" uniqKey="Gavoille C" first="Cyril" last="Gavoille">Cyril Gavoille</name>
</author>
</analytic>
<series>
<title level="j">Discrete Mathematics</title>
<idno type="ISSN">0012-365X</idno>
<imprint>
<date type="datePub">2002</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc>
<textClass>
<keywords scheme="mix" xml:lang="en">
<term>anneau à corde</term>
<term>chordal ring</term>
<term>circulant digraph</term>
<term>gossiping.</term>
<term>graph isomorphism</term>
<term>graphe circulant</term>
<term>isomorphisme de graphes</term>
<term>échange total</term>
<term>échange total.</term>
</keywords>
</textClass>
</profileDesc>
</teiHeader>
<front>
<div type="abstract" xml:lang="en">Given a circulant digraph H=(V,A) of order n and of generators \gamma_0,...,\gamma_k , 0\leq \gamma_i \leq n-1 , i=0,...,k, the bipartite incident-graph of H is a bipartite graph G=(V_1,V_2,E) of order 2n where V_1=V_2=V, and, for any , and any , \{x_1,x_2\}\in E \Leftrightarrow (x_1,x_2)\in A \Leftrightarrow \exists i \in \{0,\dots,k\} \mid x_2 = x_1 + \gamma_i \pmod{n} . Knödel graphs and Fibonacci graphs are two types of such graphs. They correspond to \gamma_i=2^i-1, and \gamma_i=F(i+1)-1 , respectively. Both graphs have been extensively studied for the purpose of fast communications in networks, and they have deserved a lot of attention in this context. In this paper, we show that there exists a polynomial-time algorithm to recognize Knödel graphs, and that the same technique applies to Fibonacci graphs. The algorithm is based on a characterization of the cycles of length six in these graphs (bipartite incident-graphs of circulant digraphs always have cycles of length six). A consequence of our result is that none of the Knödel graphs are edge-transitive, apart those of 2^k-2 vertices. An open problem that arises in this field is to know whether a polynomial-time algorithm exists for any infinite family of bipartite incident-graphs of circulant digraphs indexed by their number of vertices.</div>
</front>
</TEI>
<hal api="V3">
<titleStmt>
<title xml:lang="it">Recognizing Knödel graphs</title>
<author role="aut">
<persName>
<forename type="first">Johanne</forename>
<surname>Cohen</surname>
</persName>
<email>Johanne.Cohen@loria.fr</email>
<idno type="idhal">johanne-cohen</idno>
<idno type="halauthor">130677</idno>
<orgName ref="#struct-441569"></orgName>
<affiliation ref="#struct-2363"></affiliation>
</author>
<author role="aut">
<persName>
<forename type="first">Pierre</forename>
<surname>Fraigniaud</surname>
</persName>
<email></email>
<idno type="halauthor">130082</idno>
<orgName ref="#struct-364576"></orgName>
</author>
<author role="aut">
<persName>
<forename type="first">Cyril</forename>
<surname>Gavoille</surname>
</persName>
<email></email>
<idno type="halauthor">132176</idno>
<orgName ref="#struct-365238"></orgName>
</author>
<editor role="depositor">
<persName>
<forename>Publications</forename>
<surname>Loria</surname>
</persName>
<email>publications@loria.fr</email>
</editor>
</titleStmt>
<editionStmt>
<edition n="v1" type="current">
<date type="whenSubmitted">2006-09-26 14:53:13</date>
<date type="whenModified">2016-05-19 01:09:09</date>
<date type="whenReleased">2006-09-28 15:22:47</date>
<date type="whenProduced">2002</date>
</edition>
<respStmt>
<resp>contributor</resp>
<name key="108626">
<persName>
<forename>Publications</forename>
<surname>Loria</surname>
</persName>
<email>publications@loria.fr</email>
</name>
</respStmt>
</editionStmt>
<publicationStmt>
<distributor>CCSD</distributor>
<idno type="halId">inria-00100969</idno>
<idno type="halUri">https://hal.inria.fr/inria-00100969</idno>
<idno type="halBibtex">cohen:inria-00100969</idno>
<idno type="halRefHtml">Discrete Mathematics, Elsevier, 2002, pp.41-62</idno>
<idno type="halRef">Discrete Mathematics, Elsevier, 2002, pp.41-62</idno>
</publicationStmt>
<seriesStmt>
<idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
<idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
<idno type="stamp" n="INPL">Institut National Polytechnique de Lorraine</idno>
<idno type="stamp" n="LORIA2">Publications du LORIA</idno>
<idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno>
<idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno>
<idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno>
<idno type="stamp" n="INRIA-LORRAINE">INRIA Nancy - Grand Est</idno>
<idno type="stamp" n="LABO-LORIA-SET" p="LORIA">LABO-LORIA-SET</idno>
</seriesStmt>
<notesStmt>
<note type="commentary">Article dans revue scientifique avec comité de lecture.</note>
<note type="audience" n="1">Not set</note>
<note type="popular" n="0">No</note>
<note type="peer" n="1">Yes</note>
</notesStmt>
<sourceDesc>
<biblStruct>
<analytic>
<title xml:lang="it">Recognizing Knödel graphs</title>
<author role="aut">
<persName>
<forename type="first">Johanne</forename>
<surname>Cohen</surname>
</persName>
<email>Johanne.Cohen@loria.fr</email>
<idno type="idHal">johanne-cohen</idno>
<idno type="halAuthorId">130677</idno>
<orgName ref="#struct-441569"></orgName>
<affiliation ref="#struct-2363"></affiliation>
</author>
<author role="aut">
<persName>
<forename type="first">Pierre</forename>
<surname>Fraigniaud</surname>
</persName>
<idno type="halAuthorId">130082</idno>
<orgName ref="#struct-364576"></orgName>
</author>
<author role="aut">
<persName>
<forename type="first">Cyril</forename>
<surname>Gavoille</surname>
</persName>
<idno type="halAuthorId">132176</idno>
<orgName ref="#struct-365238"></orgName>
</author>
</analytic>
<monogr>
<idno type="localRef">A02-R-427 || cohen02b</idno>
<idno type="halJournalId" status="VALID">12623</idno>
<idno type="issn">0012-365X</idno>
<title level="j">Discrete Mathematics</title>
<imprint>
<publisher>Elsevier</publisher>
<biblScope unit="issue">250</biblScope>
<biblScope unit="pp">41-62</biblScope>
<date type="datePub">2002</date>
</imprint>
</monogr>
</biblStruct>
</sourceDesc>
<profileDesc>
<langUsage>
<language ident="en">English</language>
</langUsage>
<textClass>
<keywords scheme="author">
<term xml:lang="en">échange total.</term>
<term xml:lang="en">isomorphisme de graphes</term>
<term xml:lang="en">gossiping.</term>
<term xml:lang="en">graph isomorphism</term>
<term xml:lang="en">circulant digraph</term>
<term xml:lang="en">chordal ring</term>
<term xml:lang="en">graphe circulant</term>
<term xml:lang="en">anneau à corde</term>
<term xml:lang="en">échange total</term>
</keywords>
<classCode scheme="halDomain" n="info.info-oh">Computer Science [cs]/Other [cs.OH]</classCode>
<classCode scheme="halTypology" n="ART">Journal articles</classCode>
</textClass>
<abstract xml:lang="en">Given a circulant digraph H=(V,A) of order n and of generators \gamma_0,...,\gamma_k , 0\leq \gamma_i \leq n-1 , i=0,...,k, the bipartite incident-graph of H is a bipartite graph G=(V_1,V_2,E) of order 2n where V_1=V_2=V, and, for any , and any , \{x_1,x_2\}\in E \Leftrightarrow (x_1,x_2)\in A \Leftrightarrow \exists i \in \{0,\dots,k\} \mid x_2 = x_1 + \gamma_i \pmod{n} . Knödel graphs and Fibonacci graphs are two types of such graphs. They correspond to \gamma_i=2^i-1, and \gamma_i=F(i+1)-1 , respectively. Both graphs have been extensively studied for the purpose of fast communications in networks, and they have deserved a lot of attention in this context. In this paper, we show that there exists a polynomial-time algorithm to recognize Knödel graphs, and that the same technique applies to Fibonacci graphs. The algorithm is based on a characterization of the cycles of length six in these graphs (bipartite incident-graphs of circulant digraphs always have cycles of length six). A consequence of our result is that none of the Knödel graphs are edge-transitive, apart those of 2^k-2 vertices. An open problem that arises in this field is to know whether a polynomial-time algorithm exists for any infinite family of bipartite incident-graphs of circulant digraphs indexed by their number of vertices.</abstract>
</profileDesc>
</hal>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Hal/Checkpoint
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 005755 | SxmlIndent | more

Ou

HfdSelect -h $EXPLOR_AREA/Data/Hal/Checkpoint/biblio.hfd -nk 005755 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Wicri/Lorraine
   |area=    InforLorV4
   |flux=    Hal
   |étape=   Checkpoint
   |type=    RBID
   |clé=     Hal:inria-00100969
   |texte=   Recognizing Knödel graphs
}}

Wicri

This area was generated with Dilib version V0.6.33.
Data generation: Mon Jun 10 21:56:28 2019. Site generation: Fri Feb 25 15:29:27 2022