On Maximal Det-Independent (Res-Independent) Sets in Graphs

In this writing, we point out some errors made in Boutin (Graphs Combin 25:789–806, 2009), where the author claims that a maximal independent set in a hereditary system is a minimal determining (resolving) set. Further more, the author claims that if the exchange property holds at the level of minim...

Full description

Saved in:
Bibliographic Details
Published inGraphs and combinatorics Vol. 38; no. 2
Main Authors Zill-E-Shams, Salman, Muhammad, Ali, Usman
Format Journal Article
LanguageEnglish
Published Tokyo Springer Japan 01.04.2022
Springer Nature B.V
Subjects
Online AccessGet full text
ISSN0911-0119
1435-5914
1435-5914
DOI10.1007/s00373-021-02452-0

Cover

Abstract In this writing, we point out some errors made in Boutin (Graphs Combin 25:789–806, 2009), where the author claims that a maximal independent set in a hereditary system is a minimal determining (resolving) set. Further more, the author claims that if the exchange property holds at the level of minimal resolving sets, then, the corresponding hereditary system is a matroid. We give counter examples to disprove both of her claims. Besides, we prove that there exist graphs having such maximal independent sets which are not necessarily determining (resolving) sets. Also, we give necessary and sufficient conditions for a class of graphs to have a maximal independent set which is not minimal determining (resolving).
AbstractList In this writing, we point out some errors made in Boutin (Graphs Combin 25:789–806, 2009), where the author claims that a maximal independent set in a hereditary system is a minimal determining (resolving) set. Further more, the author claims that if the exchange property holds at the level of minimal resolving sets, then, the corresponding hereditary system is a matroid. We give counter examples to disprove both of her claims. Besides, we prove that there exist graphs having such maximal independent sets which are not necessarily determining (resolving) sets. Also, we give necessary and sufficient conditions for a class of graphs to have a maximal independent set which is not minimal determining (resolving).
ArticleNumber 44
Author Salman, Muhammad
Ali, Usman
Zill-E-Shams
Author_xml – sequence: 1
  surname: Zill-E-Shams
  fullname: Zill-E-Shams
  organization: Centre for Advanced Studies in Pure and Applied Mathematics (CASPAM), Bahauddin Zakaryia University, Department of Mathematics, The Women University
– sequence: 2
  givenname: Muhammad
  surname: Salman
  fullname: Salman, Muhammad
  organization: Department of Mathematics, The Islamia University of Bahawalpur
– sequence: 3
  givenname: Usman
  orcidid: 0000-0003-0084-5954
  surname: Ali
  fullname: Ali, Usman
  email: uali@bzu.edu.pk
  organization: Centre for Advanced Studies in Pure and Applied Mathematics (CASPAM), Bahauddin Zakaryia University, Institute de Mathematiques de Jussieu-Paris Rive Gauche
BookMark eNqNj01LAzEQhoNUsK3-AU8LXvSwOvnYpsGTVK1CpeDHOUx3s7plza5JivbfG92C4qF4mBnIvO_kfQakZxtrCDmkcEoB5JkH4JKnwGgskbEUdkifCp6lmaKiR_qgaFxRqvbIwPslAGRUQJ-cz21yhx_VK9bJpQnprS1Ma2KzITm-N_73w0nyYIJPKptMHbYvfp_sllh7c7CZQ_J0ffU4uUln8-nt5GKW5lzJkLJxWQpYMCoM8GKUM0RFJS0wV0wsUBqeQ1lKXCAXvCyyEnnBxkYImSHNleBDwru7K9vi-h3rWrcuJnZrTUF_8euOX0d-_c2vIbqOOlfrmreV8UEvm5WzMahmIyZGckxVFlXjTpW7xntnSp1XAUPV2OCwqrd_wP5Y_5Vqw-Kj2D4b95Nqi-sTX7qLsw
CitedBy_id crossref_primary_10_52280_pujm_2023_55_11_12__01
Cites_doi 10.1007/s00373-010-0880-6
10.1016/S0166-218X(00)00198-0
10.37236/1104
10.1137/050641867
ContentType Journal Article
Copyright The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature 2022
The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature 2022.
Copyright_xml – notice: The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature 2022
– notice: The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature 2022.
DBID AAYXX
CITATION
7SC
7TB
8FD
FR3
JQ2
KR7
L7M
L~C
L~D
ADTOC
UNPAY
DOI 10.1007/s00373-021-02452-0
DatabaseName CrossRef
Computer and Information Systems Abstracts
Mechanical & Transportation Engineering Abstracts
Technology Research Database
Engineering Research Database
ProQuest Computer Science Collection
Civil Engineering Abstracts
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
Unpaywall for CDI: Periodical Content
Unpaywall
DatabaseTitle CrossRef
Civil Engineering Abstracts
Technology Research Database
Computer and Information Systems Abstracts – Academic
Mechanical & Transportation Engineering Abstracts
ProQuest Computer Science Collection
Computer and Information Systems Abstracts
Engineering Research Database
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts Professional
DatabaseTitleList Civil Engineering Abstracts

Database_xml – sequence: 1
  dbid: UNPAY
  name: Unpaywall
  url: https://proxy.k.utb.cz/login?url=https://unpaywall.org/
  sourceTypes: Open Access Repository
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 1435-5914
ExternalDocumentID oai:HAL:hal-03250074v1
10_1007_s00373_021_02452_0
GroupedDBID -52
-5D
-5G
-BR
-EM
-Y2
-~C
-~X
.86
.VR
06D
0R~
0VY
1N0
1SB
203
28-
29I
2J2
2JN
2JY
2KG
2KM
2LR
2P1
2VQ
2~H
30V
4.4
406
408
409
40D
40E
5GY
5QI
5VS
67Z
6NX
78A
8TC
95-
95.
95~
96X
AABHQ
AACDK
AAHNG
AAIAL
AAJBT
AAJKR
AANZL
AARHV
AARTL
AASML
AATNV
AATVU
AAUYE
AAWCG
AAYIU
AAYQN
AAYTO
AAYZH
ABAKF
ABBBX
ABBXA
ABDBF
ABDZT
ABECU
ABFTV
ABHLI
ABHQN
ABJNI
ABJOX
ABKCH
ABKTR
ABMNI
ABMQK
ABNWP
ABQBU
ABQSL
ABSXP
ABTEG
ABTHY
ABTKH
ABTMW
ABULA
ABWNU
ABXPI
ACAOD
ACBXY
ACDTI
ACGFS
ACGOD
ACHSB
ACHXU
ACIWK
ACKNC
ACMDZ
ACMLO
ACOKC
ACOMO
ACPIV
ACUHS
ACZOJ
ADHHG
ADHIR
ADIMF
ADINQ
ADKNI
ADKPE
ADRFC
ADTPH
ADURQ
ADYFF
ADZKW
AEBTG
AEFIE
AEFQL
AEGAL
AEGNC
AEJHL
AEJRE
AEKMD
AEMSY
AENEX
AEOHA
AEPYU
AESKC
AETLH
AEVLU
AEXYK
AFBBN
AFEXP
AFFNX
AFGCZ
AFLOW
AFQWF
AFWTZ
AFZKB
AGAYW
AGDGC
AGGDS
AGJBK
AGMZJ
AGQEE
AGQMX
AGRTI
AGWIL
AGWZB
AGYKE
AHAVH
AHBYD
AHKAY
AHSBF
AHYZX
AIAKS
AIGIU
AIIXL
AILAN
AITGF
AJBLW
AJRNO
AJZVZ
ALMA_UNASSIGNED_HOLDINGS
ALWAN
AMKLP
AMXSW
AMYLF
AMYQR
AOCGG
ARMRJ
ASPBG
AVWKF
AXYYD
AYJHY
AZFZN
B-.
B0M
BA0
BAPOH
BBWZM
BDATZ
BGNMA
BSONS
CAG
COF
CS3
CSCUP
DDRTE
DL5
DNIVK
DPUIP
DU5
EAD
EAP
EBLON
EBS
EIOEI
EJD
EMK
EPL
ESBYG
ESX
FEDTE
FERAY
FFXSO
FIGPU
FINBP
FNLPD
FRRFC
FSGXE
FWDCC
GGCAI
GGRSB
GJIRD
GNWQR
GQ6
GQ7
GQ8
GXS
H13
HF~
HG5
HG6
HMJXF
HQYDN
HRMNR
HVGLF
HZ~
I-F
I09
IHE
IJ-
IKXTQ
ITM
IWAJR
IXC
IZIGR
IZQ
I~X
I~Z
J-C
J0Z
JBSCW
JCJTX
JZLTJ
KDC
KOV
KOW
LAS
LLZTM
M4Y
MA-
N2Q
N9A
NB0
NDZJH
NPVJJ
NQJWS
NU0
O9-
O93
O9G
O9I
O9J
OAM
P19
P2P
P9R
PF0
PQQKQ
PT4
PT5
Q2X
QOK
QOS
R4E
R89
R9I
RHV
RNI
ROL
RPX
RSV
RZK
S16
S1Z
S26
S27
S28
S3B
SAP
SCLPG
SDD
SDH
SDM
SHX
SISQX
SJYHP
SMT
SNE
SNPRN
SNX
SOHCF
SOJ
SPISZ
SRMVM
SSLCW
STPWE
SZN
T13
T16
TN5
TSG
TSK
TSV
TUC
TUS
U2A
UG4
UOJIU
UTJUX
UZXMN
VC2
VFIZW
W23
W48
WIP
WK8
YLTOR
Z45
Z7U
Z7X
Z83
Z87
Z88
Z8O
Z8R
Z8W
Z91
ZMTXR
ZWQNP
~8M
~A9
~EX
88I
AAPKM
AAYXX
ABBRH
ABDBE
ABFSG
ABJCF
ABRTQ
ACSTC
ADHKG
AEZWR
AFDZB
AFHIU
AFOHR
AGQPQ
AHPBZ
AHWEU
AIXLP
AMVHM
ATHPR
AYFIA
BGLVJ
CCPQU
CITATION
K7-
M2P
M7S
PHGZM
PHGZT
PQGLB
PTHSS
7SC
7TB
8FD
FR3
JQ2
KR7
L7M
L~C
L~D
ADTOC
UNPAY
ID FETCH-LOGICAL-c397t-28ff40b214e03d6c2aa9171dac924ba7e3c0ff7aba343fd5fa3d28e4475a1c943
IEDL.DBID UNPAY
ISSN 0911-0119
1435-5914
IngestDate Sun Oct 26 04:15:04 EDT 2025
Wed Sep 17 23:55:40 EDT 2025
Thu Apr 24 23:02:05 EDT 2025
Wed Oct 01 03:23:33 EDT 2025
Fri Feb 21 02:47:37 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 2
Keywords Resolving set
Independent set
Hereditary system
05C12
05B35
Determining set
Language English
License other-oa
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c397t-28ff40b214e03d6c2aa9171dac924ba7e3c0ff7aba343fd5fa3d28e4475a1c943
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0003-0084-5954
OpenAccessLink https://proxy.k.utb.cz/login?url=https://hal.sorbonne-universite.fr/hal-03250074
PQID 2624678195
PQPubID 30813
ParticipantIDs unpaywall_primary_10_1007_s00373_021_02452_0
proquest_journals_2624678195
crossref_citationtrail_10_1007_s00373_021_02452_0
crossref_primary_10_1007_s00373_021_02452_0
springer_journals_10_1007_s00373_021_02452_0
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2022-04-01
PublicationDateYYYYMMDD 2022-04-01
PublicationDate_xml – month: 04
  year: 2022
  text: 2022-04-01
  day: 01
PublicationDecade 2020
PublicationPlace Tokyo
PublicationPlace_xml – name: Tokyo
PublicationTitle Graphs and combinatorics
PublicationTitleAbbrev Graphs and Combinatorics
PublicationYear 2022
Publisher Springer Japan
Springer Nature B.V
Publisher_xml – name: Springer Japan
– name: Springer Nature B.V
References Ćaceres, Hernando, Mora, Pelayo, Puertas, Seara, Wood (CR3) 2007; 21
West (CR7) 1996
Chartrand, Eroh, Johnson, Oellermann (CR4) 2000; 105
Javaid, Fazil, Ali, Salman (CR6) 2018; 14
Boutin (CR1) 2009; 25
Hernando, Mora, Pelayo, Seera, Wood (CR5) 2010; 2010
Boutin (CR2) 2006; 13
G Chartrand (2452_CR4) 2000; 105
C Hernando (2452_CR5) 2010; 2010
J Ćaceres (2452_CR3) 2007; 21
DL Boutin (2452_CR1) 2009; 25
I Javaid (2452_CR6) 2018; 14
DB West (2452_CR7) 1996
DL Boutin (2452_CR2) 2006; 13
References_xml – volume: 14
  start-page: 1
  year: 2018
  end-page: 12
  ident: CR6
  article-title: On some parameters related to fixing sets in graphs
  publication-title: J. Prime Res. Math.
– volume: 2010
  start-page: 17
  year: 2010
  ident: CR5
  article-title: Extremal graph theory for metric dimension and diameter
  publication-title: Electron. J. Combin.
– volume: 25
  start-page: 789
  year: 2009
  end-page: 806
  ident: CR1
  article-title: Determining sets, resolving sets and the exchange property
  publication-title: Graphs Combin.
  doi: 10.1007/s00373-010-0880-6
– volume: 105
  start-page: 99
  issue: 1–3
  year: 2000
  end-page: 113
  ident: CR4
  article-title: Resolvability in graphs and the metric dimension of a graph
  publication-title: Discrete Appl. Math.
  doi: 10.1016/S0166-218X(00)00198-0
– volume: 13
  start-page: 1
  year: 2006
  end-page: 12
  ident: CR2
  article-title: Identifying graph automorphism using determining sets
  publication-title: Electron. J. Combin.
  doi: 10.37236/1104
– volume: 21
  start-page: 423
  year: 2007
  end-page: 441
  ident: CR3
  article-title: On the metric dimension of Cartesian products of graphs
  publication-title: SIAM J. Discrete Math.
  doi: 10.1137/050641867
– year: 1996
  ident: CR7
  publication-title: Introduction to Graph Theory
– volume: 21
  start-page: 423
  year: 2007
  ident: 2452_CR3
  publication-title: SIAM J. Discrete Math.
  doi: 10.1137/050641867
– volume: 2010
  start-page: 17
  year: 2010
  ident: 2452_CR5
  publication-title: Electron. J. Combin.
– volume-title: Introduction to Graph Theory
  year: 1996
  ident: 2452_CR7
– volume: 14
  start-page: 1
  year: 2018
  ident: 2452_CR6
  publication-title: J. Prime Res. Math.
– volume: 25
  start-page: 789
  year: 2009
  ident: 2452_CR1
  publication-title: Graphs Combin.
  doi: 10.1007/s00373-010-0880-6
– volume: 105
  start-page: 99
  issue: 1–3
  year: 2000
  ident: 2452_CR4
  publication-title: Discrete Appl. Math.
  doi: 10.1016/S0166-218X(00)00198-0
– volume: 13
  start-page: 1
  year: 2006
  ident: 2452_CR2
  publication-title: Electron. J. Combin.
  doi: 10.37236/1104
SSID ssj0005140
Score 2.2511456
Snippet In this writing, we point out some errors made in Boutin (Graphs Combin 25:789–806, 2009), where the author claims that a maximal independent set in a...
SourceID unpaywall
proquest
crossref
springer
SourceType Open Access Repository
Aggregation Database
Enrichment Source
Index Database
Publisher
SubjectTerms Combinatorics
Engineering Design
Graphs
Mathematics
Mathematics and Statistics
Original Paper
SummonAdditionalLinks – databaseName: SpringerLink Journals (ICM)
  dbid: U2A
  link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8NAEF6kHtSD-MRqlT14UOxC9pEXnopaq1AFtdBb2CcUaiwmRf337qZJWkGKXpPdCcxsduZjZr4B4DTWYcR9nyKOsUEsoBgJTxLETCiUUDqSRSNt_yHoDdj90B-WTWFZVe1epSSLm7pudnNUKS7naOGvSxciC9RXfUfnZU_xgHTmhR2zNkjrCB1QxnHZKvO7jJ_uaB5j1mnRDbA2TSf864OPxwuep7sFNsuQEXZmNt4GKzrdARv9mm812wWXjyns88_Rq113rXN0Vw-3zeHZk84WH5zDZ51ncJTCW0dWne2BQffm5aqHyrEISNrgIUckMoZ5gmCmPaoCSTi3mAsrLi2WEjzUVHrGhFxwyqhRvuFUkUg7Zj-OZczoPmikb6k-AJDEREXSAkk_xEy42S8s5gbrINZMRSRsAlxpJ5ElZ7gbXTFOarbjQqOJ1WhSaDTxmuCi3jOZMWYsXd2qlJ6Uf0-WkIDY-9tl-JqgXRli_nqZtHZtrD98_PB_0o_AOnHND0XdTgs08vepPrYhSS5OihP4DVaE0d8
  priority: 102
  providerName: Springer Nature
Title On Maximal Det-Independent (Res-Independent) Sets in Graphs
URI https://link.springer.com/article/10.1007/s00373-021-02452-0
https://www.proquest.com/docview/2624678195
https://hal.sorbonne-universite.fr/hal-03250074
UnpaywallVersion submittedVersion
Volume 38
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVEBS
  databaseName: EBSCOhost Academic Search Ultimate
  customDbUrl: https://search.ebscohost.com/login.aspx?authtype=ip,shib&custid=s3936755&profile=ehost&defaultdb=asn
  eissn: 1435-5914
  dateEnd: 20241102
  omitProxy: true
  ssIdentifier: ssj0005140
  issn: 0911-0119
  databaseCode: ABDBF
  dateStart: 20030601
  isFulltext: true
  titleUrlDefault: https://search.ebscohost.com/direct.asp?db=asn
  providerName: EBSCOhost
– providerCode: PRVEBS
  databaseName: EBSCOhost Mathematics Source - HOST
  customDbUrl:
  eissn: 1435-5914
  dateEnd: 20241102
  omitProxy: false
  ssIdentifier: ssj0005140
  issn: 0911-0119
  databaseCode: AMVHM
  dateStart: 19851201
  isFulltext: true
  titleUrlDefault: https://www.ebsco.com/products/research-databases/mathematics-source
  providerName: EBSCOhost
– providerCode: PRVLSH
  databaseName: SpringerLink Journals
  customDbUrl:
  mediaType: online
  eissn: 1435-5914
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0005140
  issn: 0911-0119
  databaseCode: AFBBN
  dateStart: 19851201
  isFulltext: true
  providerName: Library Specific Holdings
– providerCode: PRVAVX
  databaseName: SpringerLINK - Czech Republic Consortium
  customDbUrl:
  eissn: 1435-5914
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0005140
  issn: 0911-0119
  databaseCode: AGYKE
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: http://link.springer.com
  providerName: Springer Nature
– providerCode: PRVAVX
  databaseName: SpringerLink Journals (ICM)
  customDbUrl:
  eissn: 1435-5914
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0005140
  issn: 0911-0119
  databaseCode: U2A
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: http://www.springerlink.com/journals/
  providerName: Springer Nature
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1JT9tAFH6C5EA5lKVFhIbIhx6oygTP4k2cwhKWKhS1jQQna2Y8o6IGE8WOWH49M45tlgMqJ0ueZ3vsb6z3jd573wP4Gqkg5J5HEcdYI-ZTjIQrCWI6EIlIVCiLQtrBmX88ZKcX3sUc7FS1MH8N48xuJsJmeaBplZugunpih5BLjcs2Xm8emr5nyHcDmsOz895loahXVIgVrTwsCUBehFlZJlMUy1mpFRuzNFY23Ijcl67oiV_WIdFFWJimY35_y0ejZ16nvwTn1XxnySb_utNcdOXDKynHd7zQMnwsGajTmy2ZFZhT6SosDmr51uwT7P5MnQG_u7o2dgcqRyd1r9zc2fqlsucnvjm_VZ45V6lzZLWvs88w7B_-2T9GZZcFJA0XyREJtWauIJgplya-JJybLRxOuDRbM8EDRaWrdcAFp4zqxNOcJiRUViiQYxkxugaN9CZV6-CQiCShNPtSL8BM2FYyLOIaKz9SLAlJ0AJcffBYlhLkthPGKK7FkwuQYgNSXIAUuy34Xl8znglwvGndrnCMy58xi4lPjDuwAcMWbFfYPg2_dbftGv__ePjG-8y_wAdiaymKNKA2NPLJVG0ahpOLDjR7ewd7fXs8uvxx2IH5Iel1yrX-COEk9Lg
linkProvider Unpaywall
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT8MwDLbQOAwOvBHj2QMHEAQ1afoSJ8RjAzaQgElwqpI0kRCjINqJx68n6doOEJrg2qZu67i1P9n-DLAZSj9grusghrFC1HMw4rYgiCqfxzyWgcgbaTsXXqtLz27d26IpLC2r3cuUZP6nrprdDFWKyTlq-GvShUgD9XGqAQqpwfhB8-78eFjaMWiE1K7QQGUcFs0yv0v57pCGUWaVGJ2Eej95Zu-vrNf74ntOpqFbPvWg5ORhr5_xPfHxg9Dxv681A1NFMGodDKxnFsZkMgeTnYrJNZ2H_cvE6rC3-0e97khm6LQam5tZW1cy_Xpg27qWWWrdJ1bT0GCnC9A9Ob45bKFi4AISOizJEAmUojYnmErbiT1BGNNoDsdMaJTGmS8dYSvlM84c6qjYVcyJSSANZyDDIqTOItSSp0QugUVCEgdCQ1TXx5SbqTI0ZApLL5Q0DojfAFxqPRIFG7kZitGLKh7lXDGRVkyUKyayG7BTXfM84OIYuXq13Myo-C7TiHhEewaTO2zAbrkfw9OjpO1WRvCHmy__T_oG1Fs3nXbUPr04X4EJYlos8uqgVahlL325pgOfjK8Xdv4J7ePxsA
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8NAEF6kgtqD-MRq1Rw8KHYxu9m88FSstVVbRS30Fjb7gEKNxaSo_97dvFpBil6TzQRmNtn5mPm-AeDEF65HbduCFCEJiWMhGJoMQyLdkIdceCwl0vb6TmdAbof2cI7Fn3a7FyXJjNOgVZqi5GLC5UVJfNOyKbr-qKCwLh1CBdqXiRZKUDt6gJuzJo-MEqkORQ2akZ_TZn638fNomuWbZYm0Clan0YR-fdDxeO4Uam-A9Tx9NJpZvDfBkoi2QLVXaq_G2-DyITJ69HP0qta1RAK75aDbxDh9EvH8hTPjWSSxMYqMGy1cHe-AQfv65aoD8xEJkKlEIoHYk5KYIUZEmBZ3GKZU4S_EKVO4KqSusJgppUtDahFLcltSi2NPaJU_iphPrF1Qid4isQcM7GPuMQUqbReRUM-BIT6VSDi-INzDbg2gwjsBy_XD9RiLcVAqH6ceDZRHg9SjgVkD5-Uzk0w9Y-HqeuH0IP-S4gA7WP3LdbWvBhpFIGa3F1lrlMH6w8v3_2f9GKw8ttrBfbd_dwDWsOZEpO08dVBJ3qfiUGUqSXiUbsZvGtvZBw
linkToUnpaywall http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3JTsMwEB1BOQAHdkTZlAMHELjESzZxQuxIBQRUglNkO7ZAlICaVCxfj50mYTkguMaT9TmaN5qZNwBrkQpC7nkUcYw1Yj7FSLiSIKYDkYhEhbJopG2f-ccddnrj3QzBdtULc2cYZ_bUE7bKA_Wr2gTV0j27hFxqXLbxesMw4nuGfDdgpHN2sXtbKOoVHWLFKA9LApAXYVa2yRTNclZqxeYsjZVNNyL3uyv65Jd1SnQcRvvpM3974d3uF69zOAkX1fMOik0eWv1ctOT7DynHf7zQFEyUDNTZHWyZaRhS6QyMt2v51mwWds5Tp81f7x-N3b7K0Uk9Kzd31i9V9vXAhnOl8sy5T50jq32dzUHn8OB67xiVUxaQNFwkRyTUmrmCYKZcmviScG5COJxwaUIzwQNFpat1wAWnjOrE05wmJFRWKJBjGTE6D430KVUL4JCIJKE0cakXYCbsKBkWcY2VHymWhCRoAq4-eCxLCXI7CaMb1-LJBUixASkuQIrdJmzW5zwPBDh-tV6ucIzLnzGLiU-MO7AJwyZsVdh-Lv92ta0a_z_cfPF_5kswRmwvRVEGtAyNvNdXK4bh5GK13NUfCfzwyQ
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=On+Maximal+Det-Independent+%28Res-Independent%29+Sets+in+Graphs&rft.jtitle=Graphs+and+combinatorics&rft.au=Zill-E-Shams&rft.au=Salman%2C+Muhammad&rft.au=Ali%2C+Usman&rft.date=2022-04-01&rft.issn=0911-0119&rft.eissn=1435-5914&rft.volume=38&rft.issue=2&rft_id=info:doi/10.1007%2Fs00373-021-02452-0&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s00373_021_02452_0
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0911-0119&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0911-0119&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0911-0119&client=summon