Regular bipolar fuzzy graphs
Abstract We introduce the concepts of regular and totally regular bipolar fuzzy graphs. We prove necessary and sufficient condition under which regular bipolar fuzzy graph and totally bipolar fuzzy graph are equivalent. We introduce the notion of bipolar fuzzy line graphs and present some of their p...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Akram, Muhammad [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2011 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag London Limited 2011 |
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| Übergeordnetes Werk: |
Enthalten in: Neural computing & applications - Springer-Verlag, 1993, 21(2011), Suppl 1 vom: 27. Dez., Seite 197-205 |
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| Übergeordnetes Werk: |
volume:21 ; year:2011 ; number:Suppl 1 ; day:27 ; month:12 ; pages:197-205 |
| Links: |
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| DOI / URN: |
10.1007/s00521-011-0772-6 |
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OLC2025584539 |
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| 520 | |a Abstract We introduce the concepts of regular and totally regular bipolar fuzzy graphs. We prove necessary and sufficient condition under which regular bipolar fuzzy graph and totally bipolar fuzzy graph are equivalent. We introduce the notion of bipolar fuzzy line graphs and present some of their properties. We state a necessary and sufficient condition for a bipolar fuzzy graph to be isomorphic to its corresponding bipolar fuzzy line graph. We examine when an isomorphism between two bipolar fuzzy graphs follows from an isomorphism of their corresponding bipolar fuzzy line graphs. | ||
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| 650 | 4 | |a Regular bipolar fuzzy graphs | |
| 650 | 4 | |a Totally regular bipolar fuzzy graphs | |
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10.1007/s00521-011-0772-6 doi (DE-627)OLC2025584539 (DE-He213)s00521-011-0772-6-p DE-627 ger DE-627 rakwb eng 004 VZ Akram, Muhammad verfasserin aut Regular bipolar fuzzy graphs 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag London Limited 2011 Abstract We introduce the concepts of regular and totally regular bipolar fuzzy graphs. We prove necessary and sufficient condition under which regular bipolar fuzzy graph and totally bipolar fuzzy graph are equivalent. We introduce the notion of bipolar fuzzy line graphs and present some of their properties. We state a necessary and sufficient condition for a bipolar fuzzy graph to be isomorphic to its corresponding bipolar fuzzy line graph. We examine when an isomorphism between two bipolar fuzzy graphs follows from an isomorphism of their corresponding bipolar fuzzy line graphs. Bipolar fuzzy sets Bipolar fuzzy graphs Bipolar fuzzy line graphs Regular bipolar fuzzy graphs Totally regular bipolar fuzzy graphs Dudek, Wieslaw A. aut Enthalten in Neural computing & applications Springer-Verlag, 1993 21(2011), Suppl 1 vom: 27. Dez., Seite 197-205 (DE-627)165669608 (DE-600)1136944-9 (DE-576)032873050 0941-0643 nnns volume:21 year:2011 number:Suppl 1 day:27 month:12 pages:197-205 https://doi.org/10.1007/s00521-011-0772-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_4046 GBV_ILN_4277 AR 21 2011 Suppl 1 27 12 197-205 |
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10.1007/s00521-011-0772-6 doi (DE-627)OLC2025584539 (DE-He213)s00521-011-0772-6-p DE-627 ger DE-627 rakwb eng 004 VZ Akram, Muhammad verfasserin aut Regular bipolar fuzzy graphs 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag London Limited 2011 Abstract We introduce the concepts of regular and totally regular bipolar fuzzy graphs. We prove necessary and sufficient condition under which regular bipolar fuzzy graph and totally bipolar fuzzy graph are equivalent. We introduce the notion of bipolar fuzzy line graphs and present some of their properties. We state a necessary and sufficient condition for a bipolar fuzzy graph to be isomorphic to its corresponding bipolar fuzzy line graph. We examine when an isomorphism between two bipolar fuzzy graphs follows from an isomorphism of their corresponding bipolar fuzzy line graphs. Bipolar fuzzy sets Bipolar fuzzy graphs Bipolar fuzzy line graphs Regular bipolar fuzzy graphs Totally regular bipolar fuzzy graphs Dudek, Wieslaw A. aut Enthalten in Neural computing & applications Springer-Verlag, 1993 21(2011), Suppl 1 vom: 27. Dez., Seite 197-205 (DE-627)165669608 (DE-600)1136944-9 (DE-576)032873050 0941-0643 nnns volume:21 year:2011 number:Suppl 1 day:27 month:12 pages:197-205 https://doi.org/10.1007/s00521-011-0772-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_4046 GBV_ILN_4277 AR 21 2011 Suppl 1 27 12 197-205 |
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10.1007/s00521-011-0772-6 doi (DE-627)OLC2025584539 (DE-He213)s00521-011-0772-6-p DE-627 ger DE-627 rakwb eng 004 VZ Akram, Muhammad verfasserin aut Regular bipolar fuzzy graphs 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag London Limited 2011 Abstract We introduce the concepts of regular and totally regular bipolar fuzzy graphs. We prove necessary and sufficient condition under which regular bipolar fuzzy graph and totally bipolar fuzzy graph are equivalent. We introduce the notion of bipolar fuzzy line graphs and present some of their properties. We state a necessary and sufficient condition for a bipolar fuzzy graph to be isomorphic to its corresponding bipolar fuzzy line graph. We examine when an isomorphism between two bipolar fuzzy graphs follows from an isomorphism of their corresponding bipolar fuzzy line graphs. Bipolar fuzzy sets Bipolar fuzzy graphs Bipolar fuzzy line graphs Regular bipolar fuzzy graphs Totally regular bipolar fuzzy graphs Dudek, Wieslaw A. aut Enthalten in Neural computing & applications Springer-Verlag, 1993 21(2011), Suppl 1 vom: 27. Dez., Seite 197-205 (DE-627)165669608 (DE-600)1136944-9 (DE-576)032873050 0941-0643 nnns volume:21 year:2011 number:Suppl 1 day:27 month:12 pages:197-205 https://doi.org/10.1007/s00521-011-0772-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_4046 GBV_ILN_4277 AR 21 2011 Suppl 1 27 12 197-205 |
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10.1007/s00521-011-0772-6 doi (DE-627)OLC2025584539 (DE-He213)s00521-011-0772-6-p DE-627 ger DE-627 rakwb eng 004 VZ Akram, Muhammad verfasserin aut Regular bipolar fuzzy graphs 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag London Limited 2011 Abstract We introduce the concepts of regular and totally regular bipolar fuzzy graphs. We prove necessary and sufficient condition under which regular bipolar fuzzy graph and totally bipolar fuzzy graph are equivalent. We introduce the notion of bipolar fuzzy line graphs and present some of their properties. We state a necessary and sufficient condition for a bipolar fuzzy graph to be isomorphic to its corresponding bipolar fuzzy line graph. We examine when an isomorphism between two bipolar fuzzy graphs follows from an isomorphism of their corresponding bipolar fuzzy line graphs. Bipolar fuzzy sets Bipolar fuzzy graphs Bipolar fuzzy line graphs Regular bipolar fuzzy graphs Totally regular bipolar fuzzy graphs Dudek, Wieslaw A. aut Enthalten in Neural computing & applications Springer-Verlag, 1993 21(2011), Suppl 1 vom: 27. Dez., Seite 197-205 (DE-627)165669608 (DE-600)1136944-9 (DE-576)032873050 0941-0643 nnns volume:21 year:2011 number:Suppl 1 day:27 month:12 pages:197-205 https://doi.org/10.1007/s00521-011-0772-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_4046 GBV_ILN_4277 AR 21 2011 Suppl 1 27 12 197-205 |
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Abstract We introduce the concepts of regular and totally regular bipolar fuzzy graphs. We prove necessary and sufficient condition under which regular bipolar fuzzy graph and totally bipolar fuzzy graph are equivalent. We introduce the notion of bipolar fuzzy line graphs and present some of their properties. We state a necessary and sufficient condition for a bipolar fuzzy graph to be isomorphic to its corresponding bipolar fuzzy line graph. We examine when an isomorphism between two bipolar fuzzy graphs follows from an isomorphism of their corresponding bipolar fuzzy line graphs. © Springer-Verlag London Limited 2011 |
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Abstract We introduce the concepts of regular and totally regular bipolar fuzzy graphs. We prove necessary and sufficient condition under which regular bipolar fuzzy graph and totally bipolar fuzzy graph are equivalent. We introduce the notion of bipolar fuzzy line graphs and present some of their properties. We state a necessary and sufficient condition for a bipolar fuzzy graph to be isomorphic to its corresponding bipolar fuzzy line graph. We examine when an isomorphism between two bipolar fuzzy graphs follows from an isomorphism of their corresponding bipolar fuzzy line graphs. © Springer-Verlag London Limited 2011 |
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Abstract We introduce the concepts of regular and totally regular bipolar fuzzy graphs. We prove necessary and sufficient condition under which regular bipolar fuzzy graph and totally bipolar fuzzy graph are equivalent. We introduce the notion of bipolar fuzzy line graphs and present some of their properties. We state a necessary and sufficient condition for a bipolar fuzzy graph to be isomorphic to its corresponding bipolar fuzzy line graph. We examine when an isomorphism between two bipolar fuzzy graphs follows from an isomorphism of their corresponding bipolar fuzzy line graphs. © Springer-Verlag London Limited 2011 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2025584539</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230502114508.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2011 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00521-011-0772-6</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2025584539</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s00521-011-0772-6-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">004</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Akram, Muhammad</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Regular bipolar fuzzy graphs</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2011</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer-Verlag London Limited 2011</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We introduce the concepts of regular and totally regular bipolar fuzzy graphs. 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