On the Integrability of Strongly Regular Graphs View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-03-21

AUTHORS

Jack H. Koolen, Masood Ur Rehman, Qianqian Yang

ABSTRACT

Koolen et al. showed that if a connected graph with smallest eigenvalue at least -3 has large minimal valency, then it is 2-integrable. In this paper, we will prove that a lower bound for the minimal valency is 166.

PAGES

1-19

References to SciGraph publications

  • 2003-07. The Hoffman-Singleton Graph and its Automorphisms in JOURNAL OF ALGEBRAIC COMBINATORICS
  • 2001. Algebraic Graph Theory in NONE
  • 1989. Distance-Regular Graphs in NONE
  • Journal

    TITLE

    Graphs and Combinatorics

    ISSUE

    N/A

    VOLUME

    N/A

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00373-019-02032-3

    DOI

    http://dx.doi.org/10.1007/s00373-019-02032-3

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1112918606


    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", 
        "author": [
          {
            "affiliation": {
              "alternateName": "University of Science and Technology of China", 
              "id": "https://www.grid.ac/institutes/grid.59053.3a", 
              "name": [
                "Wen-Tsun Wu Key Laboratory of CAS, School of Mathematical Sciences, University of Science and Technology of China, 230026, Hefei, Anhui, People\u2019s Republic of China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Koolen", 
            "givenName": "Jack H.", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Science and Technology of China", 
              "id": "https://www.grid.ac/institutes/grid.59053.3a", 
              "name": [
                "School of Mathematical Sciences, University of Science and Technology of China, 230026, Hefei, Anhui, People\u2019s Republic of China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Rehman", 
            "givenName": "Masood Ur", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Science and Technology of China", 
              "id": "https://www.grid.ac/institutes/grid.59053.3a", 
              "name": [
                "School of Mathematical Sciences, University of Science and Technology of China, 230026, Hefei, Anhui, People\u2019s Republic of China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Yang", 
            "givenName": "Qianqian", 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1016/0097-3165(92)90001-b", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006300770"
            ], 
            "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/10.1098/rspa.1989.0124", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010477499"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1013855957", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-74341-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1013855957", 
              "https://doi.org/10.1007/978-3-642-74341-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-74341-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1013855957", 
              "https://doi.org/10.1007/978-3-642-74341-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1017906081", 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1017906081", 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1112/plms/s2-30.1.264", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018441719"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1111/j.2164-0947.1969.tb01990.x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020700241"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1025136524481", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025181551", 
              "https://doi.org/10.1023/a:1025136524481"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1025136524481", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025181551", 
              "https://doi.org/10.1023/a:1025136524481"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0021-8693(76)90162-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031009198"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0024-3795(77)90027-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036476227"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0012-365x(75)90029-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036703097"
            ], 
            "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/10.1016/0012-365x(92)90532-k", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041970418"
            ], 
            "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://doi.org/10.1147/rd.45.0497", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1063182559"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1017/cbo9780511662140", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1098679710"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4171/066", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1099455254"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.aim.2018.09.004", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1106985407"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2019-03-21", 
        "datePublishedReg": "2019-03-21", 
        "description": "Koolen et al. showed that if a connected graph with smallest eigenvalue at least -3 has large minimal valency, then it is 2-integrable. In this paper, we will prove that a lower bound for the minimal valency is 166.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s00373-019-02032-3", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136071", 
            "issn": [
              "0911-0119", 
              "1435-5914"
            ], 
            "name": "Graphs and Combinatorics", 
            "type": "Periodical"
          }
        ], 
        "name": "On the Integrability of Strongly Regular Graphs", 
        "pagination": "1-19", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "9e4ffbf5aca2293d74b7861291f94cf37606d9fbe7e2f65f146502b6f7a20de2"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s00373-019-02032-3"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1112918606"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s00373-019-02032-3", 
          "https://app.dimensions.ai/details/publication/pub.1112918606"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T12:53", 
        "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/v90/0000000364_0000000364/records_72853_00000001.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1007%2Fs00373-019-02032-3"
      }
    ]
     

    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/s00373-019-02032-3'

    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/s00373-019-02032-3'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00373-019-02032-3'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00373-019-02032-3'


     

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

    119 TRIPLES      20 PREDICATES      42 URIs      16 LITERALS      5 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s00373-019-02032-3 schema:author Nb4caea2c71af40c9af76f83d0aa7c797
    2 schema:citation sg:pub.10.1007/978-1-4613-0163-9
    3 sg:pub.10.1007/978-3-642-74341-2
    4 sg:pub.10.1023/a:1025136524481
    5 https://app.dimensions.ai/details/publication/pub.1006414857
    6 https://app.dimensions.ai/details/publication/pub.1013855957
    7 https://app.dimensions.ai/details/publication/pub.1017906081
    8 https://doi.org/10.1016/0012-365x(75)90029-1
    9 https://doi.org/10.1016/0012-365x(92)90532-k
    10 https://doi.org/10.1016/0021-8693(76)90162-9
    11 https://doi.org/10.1016/0024-3795(68)90008-6
    12 https://doi.org/10.1016/0024-3795(77)90027-1
    13 https://doi.org/10.1016/0024-3795(95)00199-2
    14 https://doi.org/10.1016/0097-3165(92)90001-b
    15 https://doi.org/10.1016/j.aim.2018.09.004
    16 https://doi.org/10.1017/cbo9780511662140
    17 https://doi.org/10.1098/rspa.1989.0124
    18 https://doi.org/10.1111/j.2164-0947.1969.tb01990.x
    19 https://doi.org/10.1112/plms/s2-30.1.264
    20 https://doi.org/10.1147/rd.45.0497
    21 https://doi.org/10.4171/066
    22 schema:datePublished 2019-03-21
    23 schema:datePublishedReg 2019-03-21
    24 schema:description Koolen et al. showed that if a connected graph with smallest eigenvalue at least -3 has large minimal valency, then it is 2-integrable. In this paper, we will prove that a lower bound for the minimal valency is 166.
    25 schema:genre research_article
    26 schema:inLanguage en
    27 schema:isAccessibleForFree false
    28 schema:isPartOf sg:journal.1136071
    29 schema:name On the Integrability of Strongly Regular Graphs
    30 schema:pagination 1-19
    31 schema:productId N153b08904d9f41af944c66a980a1f136
    32 N4de5d20393954888b655202dc2d28557
    33 Nb1ba16713e054d948a73ea5dbbba7044
    34 schema:sameAs https://app.dimensions.ai/details/publication/pub.1112918606
    35 https://doi.org/10.1007/s00373-019-02032-3
    36 schema:sdDatePublished 2019-04-11T12:53
    37 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    38 schema:sdPublisher N1986f75c6783453ea7c295a14d730279
    39 schema:url https://link.springer.com/10.1007%2Fs00373-019-02032-3
    40 sgo:license sg:explorer/license/
    41 sgo:sdDataset articles
    42 rdf:type schema:ScholarlyArticle
    43 N153b08904d9f41af944c66a980a1f136 schema:name doi
    44 schema:value 10.1007/s00373-019-02032-3
    45 rdf:type schema:PropertyValue
    46 N1986f75c6783453ea7c295a14d730279 schema:name Springer Nature - SN SciGraph project
    47 rdf:type schema:Organization
    48 N4de5d20393954888b655202dc2d28557 schema:name dimensions_id
    49 schema:value pub.1112918606
    50 rdf:type schema:PropertyValue
    51 N54a8b813521743b5b54ac7efea97b993 schema:affiliation https://www.grid.ac/institutes/grid.59053.3a
    52 schema:familyName Yang
    53 schema:givenName Qianqian
    54 rdf:type schema:Person
    55 N5ed5d1bd3fd8492899b951607359163f schema:affiliation https://www.grid.ac/institutes/grid.59053.3a
    56 schema:familyName Rehman
    57 schema:givenName Masood Ur
    58 rdf:type schema:Person
    59 N94604063b2fc4c68a985dec4560fefba rdf:first N54a8b813521743b5b54ac7efea97b993
    60 rdf:rest rdf:nil
    61 Nb1ba16713e054d948a73ea5dbbba7044 schema:name readcube_id
    62 schema:value 9e4ffbf5aca2293d74b7861291f94cf37606d9fbe7e2f65f146502b6f7a20de2
    63 rdf:type schema:PropertyValue
    64 Nb4caea2c71af40c9af76f83d0aa7c797 rdf:first Nb785e26241af40158883754df865a07e
    65 rdf:rest Ndd88eb1328594b5db70c6e98a870506c
    66 Nb785e26241af40158883754df865a07e schema:affiliation https://www.grid.ac/institutes/grid.59053.3a
    67 schema:familyName Koolen
    68 schema:givenName Jack H.
    69 rdf:type schema:Person
    70 Ndd88eb1328594b5db70c6e98a870506c rdf:first N5ed5d1bd3fd8492899b951607359163f
    71 rdf:rest N94604063b2fc4c68a985dec4560fefba
    72 sg:journal.1136071 schema:issn 0911-0119
    73 1435-5914
    74 schema:name Graphs and Combinatorics
    75 rdf:type schema:Periodical
    76 sg:pub.10.1007/978-1-4613-0163-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006414857
    77 https://doi.org/10.1007/978-1-4613-0163-9
    78 rdf:type schema:CreativeWork
    79 sg:pub.10.1007/978-3-642-74341-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013855957
    80 https://doi.org/10.1007/978-3-642-74341-2
    81 rdf:type schema:CreativeWork
    82 sg:pub.10.1023/a:1025136524481 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025181551
    83 https://doi.org/10.1023/a:1025136524481
    84 rdf:type schema:CreativeWork
    85 https://app.dimensions.ai/details/publication/pub.1006414857 schema:CreativeWork
    86 https://app.dimensions.ai/details/publication/pub.1013855957 schema:CreativeWork
    87 https://app.dimensions.ai/details/publication/pub.1017906081 schema:CreativeWork
    88 https://doi.org/10.1016/0012-365x(75)90029-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036703097
    89 rdf:type schema:CreativeWork
    90 https://doi.org/10.1016/0012-365x(92)90532-k schema:sameAs https://app.dimensions.ai/details/publication/pub.1041970418
    91 rdf:type schema:CreativeWork
    92 https://doi.org/10.1016/0021-8693(76)90162-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031009198
    93 rdf:type schema:CreativeWork
    94 https://doi.org/10.1016/0024-3795(68)90008-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052573879
    95 rdf:type schema:CreativeWork
    96 https://doi.org/10.1016/0024-3795(77)90027-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036476227
    97 rdf:type schema:CreativeWork
    98 https://doi.org/10.1016/0024-3795(95)00199-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037927312
    99 rdf:type schema:CreativeWork
    100 https://doi.org/10.1016/0097-3165(92)90001-b schema:sameAs https://app.dimensions.ai/details/publication/pub.1006300770
    101 rdf:type schema:CreativeWork
    102 https://doi.org/10.1016/j.aim.2018.09.004 schema:sameAs https://app.dimensions.ai/details/publication/pub.1106985407
    103 rdf:type schema:CreativeWork
    104 https://doi.org/10.1017/cbo9780511662140 schema:sameAs https://app.dimensions.ai/details/publication/pub.1098679710
    105 rdf:type schema:CreativeWork
    106 https://doi.org/10.1098/rspa.1989.0124 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010477499
    107 rdf:type schema:CreativeWork
    108 https://doi.org/10.1111/j.2164-0947.1969.tb01990.x schema:sameAs https://app.dimensions.ai/details/publication/pub.1020700241
    109 rdf:type schema:CreativeWork
    110 https://doi.org/10.1112/plms/s2-30.1.264 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018441719
    111 rdf:type schema:CreativeWork
    112 https://doi.org/10.1147/rd.45.0497 schema:sameAs https://app.dimensions.ai/details/publication/pub.1063182559
    113 rdf:type schema:CreativeWork
    114 https://doi.org/10.4171/066 schema:sameAs https://app.dimensions.ai/details/publication/pub.1099455254
    115 rdf:type schema:CreativeWork
    116 https://www.grid.ac/institutes/grid.59053.3a schema:alternateName University of Science and Technology of China
    117 schema:name School of Mathematical Sciences, University of Science and Technology of China, 230026, Hefei, Anhui, People’s Republic of China
    118 Wen-Tsun Wu Key Laboratory of CAS, School of Mathematical Sciences, University of Science and Technology of China, 230026, Hefei, Anhui, People’s Republic of China
    119 rdf:type schema:Organization
     




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


    ...