Metric and Strong Metric Dimension in Cozero-Divisor Graphs
Abstract Let R be a commutative ring with non-zero identity and $$W^*(R)$$ be the set of all non-zero and non-unit elements of R. The cozero-divisor graph of R, denoted by $$\Gamma ^{\prime }(R)$$, is a graph with the vertex set $$W^*(R)$$ and two distinct vertices a and b are adjacent if and only i...
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| Autor*in: |
Nikandish, R. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Mediterranean journal of mathematics - Springer International Publishing, 2004, 18(2021), 3 vom: 20. Apr. |
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| Übergeordnetes Werk: |
volume:18 ; year:2021 ; number:3 ; day:20 ; month:04 |
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| DOI / URN: |
10.1007/s00009-021-01772-y |
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| 520 | |a Abstract Let R be a commutative ring with non-zero identity and $$W^*(R)$$ be the set of all non-zero and non-unit elements of R. The cozero-divisor graph of R, denoted by $$\Gamma ^{\prime }(R)$$, is a graph with the vertex set $$W^*(R)$$ and two distinct vertices a and b are adjacent if and only if $$a\not \in Rb$$ and $$b\not \in Ra$$. In this paper, the metric dimension and strong metric dimension of $$\Gamma ^{\prime }(R)$$ are investigated. We compute the exact values of strong metric and metric dimension in cozero-divisor graphs of reduced rings. Moreover, the metric dimension in cozero-divisor graphs of non-reduced rings is discussed. | ||
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10.1007/s00009-021-01772-y doi (DE-627)OLC2124995588 (DE-He213)s00009-021-01772-y-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Nikandish, R. verfasserin aut Metric and Strong Metric Dimension in Cozero-Divisor Graphs 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract Let R be a commutative ring with non-zero identity and $$W^*(R)$$ be the set of all non-zero and non-unit elements of R. The cozero-divisor graph of R, denoted by $$\Gamma ^{\prime }(R)$$, is a graph with the vertex set $$W^*(R)$$ and two distinct vertices a and b are adjacent if and only if $$a\not \in Rb$$ and $$b\not \in Ra$$. In this paper, the metric dimension and strong metric dimension of $$\Gamma ^{\prime }(R)$$ are investigated. We compute the exact values of strong metric and metric dimension in cozero-divisor graphs of reduced rings. Moreover, the metric dimension in cozero-divisor graphs of non-reduced rings is discussed. Metric dimension Strong metric dimension Cozero-divisor graph Commutative ring Nikmehr, M. J. aut Bakhtyiari, M. aut Enthalten in Mediterranean journal of mathematics Springer International Publishing, 2004 18(2021), 3 vom: 20. Apr. (DE-627)389869848 (DE-600)2149653-5 (DE-576)12119308X 1660-5446 nnns volume:18 year:2021 number:3 day:20 month:04 https://doi.org/10.1007/s00009-021-01772-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 AR 18 2021 3 20 04 |
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10.1007/s00009-021-01772-y doi (DE-627)OLC2124995588 (DE-He213)s00009-021-01772-y-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Nikandish, R. verfasserin aut Metric and Strong Metric Dimension in Cozero-Divisor Graphs 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract Let R be a commutative ring with non-zero identity and $$W^*(R)$$ be the set of all non-zero and non-unit elements of R. The cozero-divisor graph of R, denoted by $$\Gamma ^{\prime }(R)$$, is a graph with the vertex set $$W^*(R)$$ and two distinct vertices a and b are adjacent if and only if $$a\not \in Rb$$ and $$b\not \in Ra$$. In this paper, the metric dimension and strong metric dimension of $$\Gamma ^{\prime }(R)$$ are investigated. We compute the exact values of strong metric and metric dimension in cozero-divisor graphs of reduced rings. Moreover, the metric dimension in cozero-divisor graphs of non-reduced rings is discussed. Metric dimension Strong metric dimension Cozero-divisor graph Commutative ring Nikmehr, M. J. aut Bakhtyiari, M. aut Enthalten in Mediterranean journal of mathematics Springer International Publishing, 2004 18(2021), 3 vom: 20. Apr. (DE-627)389869848 (DE-600)2149653-5 (DE-576)12119308X 1660-5446 nnns volume:18 year:2021 number:3 day:20 month:04 https://doi.org/10.1007/s00009-021-01772-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 AR 18 2021 3 20 04 |
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Abstract Let R be a commutative ring with non-zero identity and $$W^*(R)$$ be the set of all non-zero and non-unit elements of R. The cozero-divisor graph of R, denoted by $$\Gamma ^{\prime }(R)$$, is a graph with the vertex set $$W^*(R)$$ and two distinct vertices a and b are adjacent if and only if $$a\not \in Rb$$ and $$b\not \in Ra$$. In this paper, the metric dimension and strong metric dimension of $$\Gamma ^{\prime }(R)$$ are investigated. We compute the exact values of strong metric and metric dimension in cozero-divisor graphs of reduced rings. Moreover, the metric dimension in cozero-divisor graphs of non-reduced rings is discussed. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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Abstract Let R be a commutative ring with non-zero identity and $$W^*(R)$$ be the set of all non-zero and non-unit elements of R. The cozero-divisor graph of R, denoted by $$\Gamma ^{\prime }(R)$$, is a graph with the vertex set $$W^*(R)$$ and two distinct vertices a and b are adjacent if and only if $$a\not \in Rb$$ and $$b\not \in Ra$$. In this paper, the metric dimension and strong metric dimension of $$\Gamma ^{\prime }(R)$$ are investigated. We compute the exact values of strong metric and metric dimension in cozero-divisor graphs of reduced rings. Moreover, the metric dimension in cozero-divisor graphs of non-reduced rings is discussed. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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Abstract Let R be a commutative ring with non-zero identity and $$W^*(R)$$ be the set of all non-zero and non-unit elements of R. The cozero-divisor graph of R, denoted by $$\Gamma ^{\prime }(R)$$, is a graph with the vertex set $$W^*(R)$$ and two distinct vertices a and b are adjacent if and only if $$a\not \in Rb$$ and $$b\not \in Ra$$. In this paper, the metric dimension and strong metric dimension of $$\Gamma ^{\prime }(R)$$ are investigated. We compute the exact values of strong metric and metric dimension in cozero-divisor graphs of reduced rings. Moreover, the metric dimension in cozero-divisor graphs of non-reduced rings is discussed. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2124995588</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230505103436.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230505s2021 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00009-021-01772-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2124995588</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s00009-021-01772-y-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">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Nikandish, R.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Metric and Strong Metric Dimension in Cozero-Divisor Graphs</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</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">© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Let R be a commutative ring with non-zero identity and $$W^*(R)$$ be the set of all non-zero and non-unit elements of R. The cozero-divisor graph of R, denoted by $$\Gamma ^{\prime }(R)$$, is a graph with the vertex set $$W^*(R)$$ and two distinct vertices a and b are adjacent if and only if $$a\not \in Rb$$ and $$b\not \in Ra$$. In this paper, the metric dimension and strong metric dimension of $$\Gamma ^{\prime }(R)$$ are investigated. We compute the exact values of strong metric and metric dimension in cozero-divisor graphs of reduced rings. Moreover, the metric dimension in cozero-divisor graphs of non-reduced rings is discussed.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Metric dimension</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Strong metric dimension</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Cozero-divisor graph</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Commutative ring</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Nikmehr, M. J.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Bakhtyiari, M.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Mediterranean journal of mathematics</subfield><subfield code="d">Springer International Publishing, 2004</subfield><subfield code="g">18(2021), 3 vom: 20. 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