Recognizing Bipartite Incident-Graphs of Circulant Digraphs
Identifieur interne : 004013 ( Hal/Curation ); précédent : 004012; suivant : 004014Recognizing Bipartite Incident-Graphs of Circulant Digraphs
Auteurs : Johanne Cohen [France] ; Pierre Fraigniaud ; Cyril GavoilleSource :
English descriptors
- mix :
Abstract
Given a circulant digraph $H=(V,A)$ of order $n$ and of generators $\gamma_0,\dots,\gamma_k$, $0\leq \gamma_i \leq n-1$, $i=0,\dots,k$, the {\em 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 $x_1\in V_1$, and any $x_2\in V_2$, $\{x_1,x_2\}\in E \Leftrightarrow (x_1,x_2)\in A \Leftrightarrow \exists i \in \{0,\dots,k\} \mid x_2 = x_1 + \gamma_i \pmod{n}$. \KGs\ and \FGs\ 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 \KGs, and that the same technique applies to \FGs. 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 \KGs\ 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...)
- to stream Hal, to step Corpus: Pour aller vers cette notice dans l'étape Curation :004013
Links to Exploration step
Hal:inria-00098892Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Recognizing Bipartite Incident-Graphs of Circulant Digraphs</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-00098892</idno>
<idno type="halId">inria-00098892</idno>
<idno type="halUri">https://hal.inria.fr/inria-00098892</idno>
<idno type="url">https://hal.inria.fr/inria-00098892</idno>
<date when="1999">1999</date>
<idno type="wicri:Area/Hal/Corpus">004013</idno>
<idno type="wicri:Area/Hal/Curation">004013</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en">Recognizing Bipartite Incident-Graphs of Circulant Digraphs</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>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>broadcasting</term>
<term>chordal rings</term>
<term>circulant graphs</term>
<term>diffusion</term>
<term>echange total</term>
<term>gossiping</term>
<term>graph isomorphism</term>
<term>graphes circulant</term>
<term>isomorphisme de graphes</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 $\gamma_0,\dots,\gamma_k$, $0\leq \gamma_i \leq n-1$, $i=0,\dots,k$, the {\em 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 $x_1\in V_1$, and any $x_2\in V_2$, $\{x_1,x_2\}\in E \Leftrightarrow (x_1,x_2)\in A \Leftrightarrow \exists i \in \{0,\dots,k\} \mid x_2 = x_1 + \gamma_i \pmod{n}$. \KGs\ and \FGs\ 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 \KGs, and that the same technique applies to \FGs. 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 \KGs\ 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="en">Recognizing Bipartite Incident-Graphs of Circulant Digraphs</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">130081</idno>
<orgName ref="#struct-364475"></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">130083</idno>
<orgName ref="#struct-364577"></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 08:39:57</date>
<date type="whenModified">2016-05-19 01:09:29</date>
<date type="whenReleased">2006-09-28 15:22:45</date>
<date type="whenProduced">1999</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-00098892</idno>
<idno type="halUri">https://hal.inria.fr/inria-00098892</idno>
<idno type="halBibtex">cohen:inria-00098892</idno>
<idno type="halRefHtml">P. Widmayer, G. Neyer, S. Eidenbenz. International Workshop on Graph Theoretic Concepts in Computer Science - WG'99, 1999, Ascona, Switzerland, Springer, 1665, pp.215-227, 1999, Lecture Notes in Computer Science</idno>
<idno type="halRef">P. Widmayer, G. Neyer, S. Eidenbenz. International Workshop on Graph Theoretic Concepts in Computer Science - WG'99, 1999, Ascona, Switzerland, Springer, 1665, pp.215-227, 1999, Lecture Notes in Computer Science</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">Colloque avec actes et comité de lecture.</note>
<note type="audience" n="1">Not set</note>
<note type="invited" n="0">No</note>
<note type="popular" n="0">No</note>
<note type="peer" n="1">Yes</note>
<note type="proceedings" n="1">Yes</note>
</notesStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en">Recognizing Bipartite Incident-Graphs of Circulant Digraphs</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">130081</idno>
<orgName ref="#struct-364475"></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">130083</idno>
<orgName ref="#struct-364577"></orgName>
</author>
</analytic>
<monogr><idno type="localRef">99-R-387 || cohen99a</idno>
<meeting><title>International Workshop on Graph Theoretic Concepts in Computer Science - WG'99</title>
<date type="start">1999</date>
<settlement>Ascona, Switzerland</settlement>
</meeting>
<editor>P. Widmayer, G. Neyer, S. Eidenbenz</editor>
<imprint><publisher>Springer</publisher>
<biblScope unit="serie">Lecture Notes in Computer Science</biblScope>
<biblScope unit="volume">1665</biblScope>
<biblScope unit="pp">215-227</biblScope>
<date type="datePub">1999</date>
</imprint>
</monogr>
</biblStruct>
</sourceDesc>
<profileDesc><langUsage><language ident="en">English</language>
</langUsage>
<textClass><keywords scheme="author"><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 graphs</term>
<term xml:lang="en">chordal rings</term>
<term xml:lang="en">broadcasting</term>
<term xml:lang="en">graphes circulant</term>
<term xml:lang="en">diffusion</term>
<term xml:lang="en">echange total</term>
</keywords>
<classCode scheme="halDomain" n="info.info-oh">Computer Science [cs]/Other [cs.OH]</classCode>
<classCode scheme="halTypology" n="COMM">Conference papers</classCode>
</textClass>
<abstract xml:lang="en">Given a circulant digraph $H=(V,A)$ of order $n$ and of generators $\gamma_0,\dots,\gamma_k$, $0\leq \gamma_i \leq n-1$, $i=0,\dots,k$, the {\em 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 $x_1\in V_1$, and any $x_2\in V_2$, $\{x_1,x_2\}\in E \Leftrightarrow (x_1,x_2)\in A \Leftrightarrow \exists i \in \{0,\dots,k\} \mid x_2 = x_1 + \gamma_i \pmod{n}$. \KGs\ and \FGs\ 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 \KGs, and that the same technique applies to \FGs. 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 \KGs\ 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/Curation
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 004013 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Hal/Curation/biblio.hfd -nk 004013 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Lorraine |area= InforLorV4 |flux= Hal |étape= Curation |type= RBID |clé= Hal:inria-00098892 |texte= Recognizing Bipartite Incident-Graphs of Circulant Digraphs }}
![]() | This area was generated with Dilib version V0.6.33. | ![]() |