The Cyclic Edge-Connectivity of Strongly Regular Graphs View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-03-05

AUTHORS

Wenqian Zhang

ABSTRACT

Let G be a connected graph. An edge cut set M of G is a cyclic edge cut set if there are at least two components of G-M which contain a cycle. The cyclic edge-connectivity of G is the minimum cardinality of a cyclic edge cut set (if exists) of G. In this paper, we show that the cyclic edge-connectivity of a connected strongly regular graph G (not K3,3) of degree k≥3 with girth c is equal to (k-2)c, where c=3,4 or 5. Moreover, if G is not the triangular graph srg-(10, 6, 3, 4), the complete multi-partite graph K2,2,2,2 or the lattice graph srg-(16, 6, 2, 2), then each cyclic edge cut set of size (k-2)c is precisely the set of edges incident with a cycle of length c in G. More... »

PAGES

1-7

References to SciGraph publications

  • 2012. Spectra of Graphs in NONE
  • 2001. Algebraic Graph Theory in NONE
  • 1977-09. Spherical codes and designs in GEOMETRIAE DEDICATA
  • 1979-12. Strongly regular graphs with smallest eigenvalue —m in ARCHIV DER MATHEMATIK
  • 1976. Graph Theory with Applications in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00373-019-02031-4

    DOI

    http://dx.doi.org/10.1007/s00373-019-02031-4

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1112540587


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0806", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Information Systems", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/08", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Information and Computing Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Peking University", 
              "id": "https://www.grid.ac/institutes/grid.11135.37", 
              "name": [
                "School of Mathematical Sciences, Peking University, 100871, Beijing, China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Zhang", 
            "givenName": "Wenqian", 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf03187604", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001602983", 
              "https://doi.org/10.1007/bf03187604"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1006414857", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4613-0163-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006414857", 
              "https://doi.org/10.1007/978-1-4613-0163-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4613-0163-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006414857", 
              "https://doi.org/10.1007/978-1-4613-0163-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1112/jlms/s1-22.2.107", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008123880"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0195-6698(85)80030-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1013963192"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ejc.2008.07.006", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019707512"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01222774", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022048618", 
              "https://doi.org/10.1007/bf01222774"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01222774", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022048618", 
              "https://doi.org/10.1007/bf01222774"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.laa.2004.08.014", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023311813"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1032245142", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4614-1939-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032245142", 
              "https://doi.org/10.1007/978-1-4614-1939-6"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4614-1939-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032245142", 
              "https://doi.org/10.1007/978-1-4614-1939-6"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0024-3795(95)00199-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1037927312"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jcta.2012.01.001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042180548"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0095-8956(92)90004-h", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043937338"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ejc.2013.10.008", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051455369"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0024-3795(68)90008-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052573879"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1109703686", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-349-03521-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1109703686", 
              "https://doi.org/10.1007/978-1-349-03521-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-349-03521-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1109703686", 
              "https://doi.org/10.1007/978-1-349-03521-2"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2019-03-05", 
        "datePublishedReg": "2019-03-05", 
        "description": "Let G be a connected graph. An edge cut set M of G is a cyclic edge cut set if there are at least two components of G-M which contain a cycle. The cyclic edge-connectivity of G is the minimum cardinality of a cyclic edge cut set (if exists) of G. In this paper, we show that the cyclic edge-connectivity of a connected strongly regular graph G (not K3,3) of degree k\u22653 with girth c is equal to (k-2)c, where c=3,4 or 5. Moreover, if G is not the triangular graph srg-(10, 6, 3, 4), the complete multi-partite graph K2,2,2,2 or the lattice graph srg-(16, 6, 2, 2), then each cyclic edge cut set of size (k-2)c is precisely the set of edges incident with a cycle of length c in G.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s00373-019-02031-4", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136071", 
            "issn": [
              "0911-0119", 
              "1435-5914"
            ], 
            "name": "Graphs and Combinatorics", 
            "type": "Periodical"
          }
        ], 
        "name": "The Cyclic Edge-Connectivity of Strongly Regular Graphs", 
        "pagination": "1-7", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "24f0534238e9eb422f4462400f2f716be647ffb1d5726c2cd7ac4f24378d54fa"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s00373-019-02031-4"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1112540587"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s00373-019-02031-4", 
          "https://app.dimensions.ai/details/publication/pub.1112540587"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T11:01", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000352_0000000352/records_60342_00000004.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1007%2Fs00373-019-02031-4"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s00373-019-02031-4'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s00373-019-02031-4'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00373-019-02031-4'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00373-019-02031-4'


     

    This table displays all metadata directly associated to this object as RDF triples.

    107 TRIPLES      21 PREDICATES      41 URIs      16 LITERALS      5 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s00373-019-02031-4 schema:about anzsrc-for:08
    2 anzsrc-for:0806
    3 schema:author Ne983618435da49a8bc42c457d117743c
    4 schema:citation sg:pub.10.1007/978-1-349-03521-2
    5 sg:pub.10.1007/978-1-4613-0163-9
    6 sg:pub.10.1007/978-1-4614-1939-6
    7 sg:pub.10.1007/bf01222774
    8 sg:pub.10.1007/bf03187604
    9 https://app.dimensions.ai/details/publication/pub.1006414857
    10 https://app.dimensions.ai/details/publication/pub.1032245142
    11 https://app.dimensions.ai/details/publication/pub.1109703686
    12 https://doi.org/10.1016/0024-3795(68)90008-6
    13 https://doi.org/10.1016/0024-3795(95)00199-2
    14 https://doi.org/10.1016/0095-8956(92)90004-h
    15 https://doi.org/10.1016/j.ejc.2008.07.006
    16 https://doi.org/10.1016/j.ejc.2013.10.008
    17 https://doi.org/10.1016/j.jcta.2012.01.001
    18 https://doi.org/10.1016/j.laa.2004.08.014
    19 https://doi.org/10.1016/s0195-6698(85)80030-5
    20 https://doi.org/10.1112/jlms/s1-22.2.107
    21 schema:datePublished 2019-03-05
    22 schema:datePublishedReg 2019-03-05
    23 schema:description Let G be a connected graph. An edge cut set M of G is a cyclic edge cut set if there are at least two components of G-M which contain a cycle. The cyclic edge-connectivity of G is the minimum cardinality of a cyclic edge cut set (if exists) of G. In this paper, we show that the cyclic edge-connectivity of a connected strongly regular graph G (not K3,3) of degree k≥3 with girth c is equal to (k-2)c, where c=3,4 or 5. Moreover, if G is not the triangular graph srg-(10, 6, 3, 4), the complete multi-partite graph K2,2,2,2 or the lattice graph srg-(16, 6, 2, 2), then each cyclic edge cut set of size (k-2)c is precisely the set of edges incident with a cycle of length c in G.
    24 schema:genre research_article
    25 schema:inLanguage en
    26 schema:isAccessibleForFree false
    27 schema:isPartOf sg:journal.1136071
    28 schema:name The Cyclic Edge-Connectivity of Strongly Regular Graphs
    29 schema:pagination 1-7
    30 schema:productId N66deb5b771aa41c79115fcdfdfbab518
    31 Ned680456bb8b4999977259f2be5a4caf
    32 Nf98e9a4cda5a4959ac6dd96051662c89
    33 schema:sameAs https://app.dimensions.ai/details/publication/pub.1112540587
    34 https://doi.org/10.1007/s00373-019-02031-4
    35 schema:sdDatePublished 2019-04-11T11:01
    36 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    37 schema:sdPublisher N592fac1a5b2b4cd580ebcd6043f5fb82
    38 schema:url https://link.springer.com/10.1007%2Fs00373-019-02031-4
    39 sgo:license sg:explorer/license/
    40 sgo:sdDataset articles
    41 rdf:type schema:ScholarlyArticle
    42 N41b20e82165946a0b9876109df77897e schema:affiliation https://www.grid.ac/institutes/grid.11135.37
    43 schema:familyName Zhang
    44 schema:givenName Wenqian
    45 rdf:type schema:Person
    46 N592fac1a5b2b4cd580ebcd6043f5fb82 schema:name Springer Nature - SN SciGraph project
    47 rdf:type schema:Organization
    48 N66deb5b771aa41c79115fcdfdfbab518 schema:name dimensions_id
    49 schema:value pub.1112540587
    50 rdf:type schema:PropertyValue
    51 Ne983618435da49a8bc42c457d117743c rdf:first N41b20e82165946a0b9876109df77897e
    52 rdf:rest rdf:nil
    53 Ned680456bb8b4999977259f2be5a4caf schema:name readcube_id
    54 schema:value 24f0534238e9eb422f4462400f2f716be647ffb1d5726c2cd7ac4f24378d54fa
    55 rdf:type schema:PropertyValue
    56 Nf98e9a4cda5a4959ac6dd96051662c89 schema:name doi
    57 schema:value 10.1007/s00373-019-02031-4
    58 rdf:type schema:PropertyValue
    59 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
    60 schema:name Information and Computing Sciences
    61 rdf:type schema:DefinedTerm
    62 anzsrc-for:0806 schema:inDefinedTermSet anzsrc-for:
    63 schema:name Information Systems
    64 rdf:type schema:DefinedTerm
    65 sg:journal.1136071 schema:issn 0911-0119
    66 1435-5914
    67 schema:name Graphs and Combinatorics
    68 rdf:type schema:Periodical
    69 sg:pub.10.1007/978-1-349-03521-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1109703686
    70 https://doi.org/10.1007/978-1-349-03521-2
    71 rdf:type schema:CreativeWork
    72 sg:pub.10.1007/978-1-4613-0163-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006414857
    73 https://doi.org/10.1007/978-1-4613-0163-9
    74 rdf:type schema:CreativeWork
    75 sg:pub.10.1007/978-1-4614-1939-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032245142
    76 https://doi.org/10.1007/978-1-4614-1939-6
    77 rdf:type schema:CreativeWork
    78 sg:pub.10.1007/bf01222774 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022048618
    79 https://doi.org/10.1007/bf01222774
    80 rdf:type schema:CreativeWork
    81 sg:pub.10.1007/bf03187604 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001602983
    82 https://doi.org/10.1007/bf03187604
    83 rdf:type schema:CreativeWork
    84 https://app.dimensions.ai/details/publication/pub.1006414857 schema:CreativeWork
    85 https://app.dimensions.ai/details/publication/pub.1032245142 schema:CreativeWork
    86 https://app.dimensions.ai/details/publication/pub.1109703686 schema:CreativeWork
    87 https://doi.org/10.1016/0024-3795(68)90008-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052573879
    88 rdf:type schema:CreativeWork
    89 https://doi.org/10.1016/0024-3795(95)00199-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037927312
    90 rdf:type schema:CreativeWork
    91 https://doi.org/10.1016/0095-8956(92)90004-h schema:sameAs https://app.dimensions.ai/details/publication/pub.1043937338
    92 rdf:type schema:CreativeWork
    93 https://doi.org/10.1016/j.ejc.2008.07.006 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019707512
    94 rdf:type schema:CreativeWork
    95 https://doi.org/10.1016/j.ejc.2013.10.008 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051455369
    96 rdf:type schema:CreativeWork
    97 https://doi.org/10.1016/j.jcta.2012.01.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042180548
    98 rdf:type schema:CreativeWork
    99 https://doi.org/10.1016/j.laa.2004.08.014 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023311813
    100 rdf:type schema:CreativeWork
    101 https://doi.org/10.1016/s0195-6698(85)80030-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013963192
    102 rdf:type schema:CreativeWork
    103 https://doi.org/10.1112/jlms/s1-22.2.107 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008123880
    104 rdf:type schema:CreativeWork
    105 https://www.grid.ac/institutes/grid.11135.37 schema:alternateName Peking University
    106 schema:name School of Mathematical Sciences, Peking University, 100871, Beijing, China
    107 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...