On Graphs of Order n with Metric Dimension %$n-4%$
Abstract For a connected graph G, let n(G), d(G) and dim(G) denote the order, the diameter and the metric dimension of G, respectively. The twin graph %$G_\text {T}%$ is obtained from G by contracting each maximal set of vertices with the same open or close neighborhood into a vertex, respectively....
Ausführliche Beschreibung
Autor*in: |
Wang, Juan [verfasserIn] |
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Format: |
E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2023 |
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Anmerkung: |
© The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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Übergeordnetes Werk: |
Enthalten in: Graphs and combinatorics - Tokyo : Springer-Verl. Tokyo, 1985, 39(2023), 2 vom: 06. März |
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Übergeordnetes Werk: |
volume:39 ; year:2023 ; number:2 ; day:06 ; month:03 |
Links: |
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DOI / URN: |
10.1007/s00373-023-02627-x |
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Katalog-ID: |
SPR049558188 |
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245 | 1 | 0 | |a On Graphs of Order n with Metric Dimension %$n-4%$ |
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520 | |a Abstract For a connected graph G, let n(G), d(G) and dim(G) denote the order, the diameter and the metric dimension of G, respectively. The twin graph %$G_\text {T}%$ is obtained from G by contracting each maximal set of vertices with the same open or close neighborhood into a vertex, respectively. In this paper, we propose a necessary and sufficient condition obtaining G from %$G_\text {T}%$ and characterize all graphs with dim%$(G)=n-4%$ and %$n(G_\text {T})=4%$ by this condition. For the graphs with dim%$(G)=n-4%$, we show the following results: (a) %$4\le n(G_\text {T})\le 7%$ if %$d(G)=3%$ and the bounds are sharp; (b) %$4\le n(G_\text {T})\le 9%$ if %$d(G)=2%$. | ||
650 | 4 | |a Resolving set |7 (dpeaa)DE-He213 | |
650 | 4 | |a Metric dimension |7 (dpeaa)DE-He213 | |
650 | 4 | |a Extremal graph |7 (dpeaa)DE-He213 | |
650 | 4 | |a Metric matrix |7 (dpeaa)DE-He213 | |
700 | 1 | |a Tian, Fenglei |4 aut | |
700 | 1 | |a Liu, Yunlong |4 aut | |
700 | 1 | |a Pang, Jingru |4 aut | |
700 | 1 | |a Miao, Lianying |4 aut | |
773 | 0 | 8 | |i Enthalten in |t Graphs and combinatorics |d Tokyo : Springer-Verl. Tokyo, 1985 |g 39(2023), 2 vom: 06. März |w (DE-627)30018381X |w (DE-600)1481435-3 |x 1435-5914 |7 nnns |
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10.1007/s00373-023-02627-x doi (DE-627)SPR049558188 (SPR)s00373-023-02627-x-e DE-627 ger DE-627 rakwb eng Wang, Juan verfasserin (orcid)0000-0002-9937-7590 aut On Graphs of Order n with Metric Dimension %$n-4%$ 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract For a connected graph G, let n(G), d(G) and dim(G) denote the order, the diameter and the metric dimension of G, respectively. The twin graph %$G_\text {T}%$ is obtained from G by contracting each maximal set of vertices with the same open or close neighborhood into a vertex, respectively. In this paper, we propose a necessary and sufficient condition obtaining G from %$G_\text {T}%$ and characterize all graphs with dim%$(G)=n-4%$ and %$n(G_\text {T})=4%$ by this condition. For the graphs with dim%$(G)=n-4%$, we show the following results: (a) %$4\le n(G_\text {T})\le 7%$ if %$d(G)=3%$ and the bounds are sharp; (b) %$4\le n(G_\text {T})\le 9%$ if %$d(G)=2%$. Resolving set (dpeaa)DE-He213 Metric dimension (dpeaa)DE-He213 Extremal graph (dpeaa)DE-He213 Metric matrix (dpeaa)DE-He213 Tian, Fenglei aut Liu, Yunlong aut Pang, Jingru aut Miao, Lianying aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 2 vom: 06. März (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:2 day:06 month:03 https://dx.doi.org/10.1007/s00373-023-02627-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 2 06 03 |
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10.1007/s00373-023-02627-x doi (DE-627)SPR049558188 (SPR)s00373-023-02627-x-e DE-627 ger DE-627 rakwb eng Wang, Juan verfasserin (orcid)0000-0002-9937-7590 aut On Graphs of Order n with Metric Dimension %$n-4%$ 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract For a connected graph G, let n(G), d(G) and dim(G) denote the order, the diameter and the metric dimension of G, respectively. The twin graph %$G_\text {T}%$ is obtained from G by contracting each maximal set of vertices with the same open or close neighborhood into a vertex, respectively. In this paper, we propose a necessary and sufficient condition obtaining G from %$G_\text {T}%$ and characterize all graphs with dim%$(G)=n-4%$ and %$n(G_\text {T})=4%$ by this condition. For the graphs with dim%$(G)=n-4%$, we show the following results: (a) %$4\le n(G_\text {T})\le 7%$ if %$d(G)=3%$ and the bounds are sharp; (b) %$4\le n(G_\text {T})\le 9%$ if %$d(G)=2%$. Resolving set (dpeaa)DE-He213 Metric dimension (dpeaa)DE-He213 Extremal graph (dpeaa)DE-He213 Metric matrix (dpeaa)DE-He213 Tian, Fenglei aut Liu, Yunlong aut Pang, Jingru aut Miao, Lianying aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 2 vom: 06. März (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:2 day:06 month:03 https://dx.doi.org/10.1007/s00373-023-02627-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 2 06 03 |
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10.1007/s00373-023-02627-x doi (DE-627)SPR049558188 (SPR)s00373-023-02627-x-e DE-627 ger DE-627 rakwb eng Wang, Juan verfasserin (orcid)0000-0002-9937-7590 aut On Graphs of Order n with Metric Dimension %$n-4%$ 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract For a connected graph G, let n(G), d(G) and dim(G) denote the order, the diameter and the metric dimension of G, respectively. The twin graph %$G_\text {T}%$ is obtained from G by contracting each maximal set of vertices with the same open or close neighborhood into a vertex, respectively. In this paper, we propose a necessary and sufficient condition obtaining G from %$G_\text {T}%$ and characterize all graphs with dim%$(G)=n-4%$ and %$n(G_\text {T})=4%$ by this condition. For the graphs with dim%$(G)=n-4%$, we show the following results: (a) %$4\le n(G_\text {T})\le 7%$ if %$d(G)=3%$ and the bounds are sharp; (b) %$4\le n(G_\text {T})\le 9%$ if %$d(G)=2%$. Resolving set (dpeaa)DE-He213 Metric dimension (dpeaa)DE-He213 Extremal graph (dpeaa)DE-He213 Metric matrix (dpeaa)DE-He213 Tian, Fenglei aut Liu, Yunlong aut Pang, Jingru aut Miao, Lianying aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 2 vom: 06. März (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:2 day:06 month:03 https://dx.doi.org/10.1007/s00373-023-02627-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 2 06 03 |
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10.1007/s00373-023-02627-x doi (DE-627)SPR049558188 (SPR)s00373-023-02627-x-e DE-627 ger DE-627 rakwb eng Wang, Juan verfasserin (orcid)0000-0002-9937-7590 aut On Graphs of Order n with Metric Dimension %$n-4%$ 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract For a connected graph G, let n(G), d(G) and dim(G) denote the order, the diameter and the metric dimension of G, respectively. The twin graph %$G_\text {T}%$ is obtained from G by contracting each maximal set of vertices with the same open or close neighborhood into a vertex, respectively. In this paper, we propose a necessary and sufficient condition obtaining G from %$G_\text {T}%$ and characterize all graphs with dim%$(G)=n-4%$ and %$n(G_\text {T})=4%$ by this condition. For the graphs with dim%$(G)=n-4%$, we show the following results: (a) %$4\le n(G_\text {T})\le 7%$ if %$d(G)=3%$ and the bounds are sharp; (b) %$4\le n(G_\text {T})\le 9%$ if %$d(G)=2%$. Resolving set (dpeaa)DE-He213 Metric dimension (dpeaa)DE-He213 Extremal graph (dpeaa)DE-He213 Metric matrix (dpeaa)DE-He213 Tian, Fenglei aut Liu, Yunlong aut Pang, Jingru aut Miao, Lianying aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 2 vom: 06. März (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:2 day:06 month:03 https://dx.doi.org/10.1007/s00373-023-02627-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 2 06 03 |
allfieldsSound |
10.1007/s00373-023-02627-x doi (DE-627)SPR049558188 (SPR)s00373-023-02627-x-e DE-627 ger DE-627 rakwb eng Wang, Juan verfasserin (orcid)0000-0002-9937-7590 aut On Graphs of Order n with Metric Dimension %$n-4%$ 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract For a connected graph G, let n(G), d(G) and dim(G) denote the order, the diameter and the metric dimension of G, respectively. The twin graph %$G_\text {T}%$ is obtained from G by contracting each maximal set of vertices with the same open or close neighborhood into a vertex, respectively. In this paper, we propose a necessary and sufficient condition obtaining G from %$G_\text {T}%$ and characterize all graphs with dim%$(G)=n-4%$ and %$n(G_\text {T})=4%$ by this condition. For the graphs with dim%$(G)=n-4%$, we show the following results: (a) %$4\le n(G_\text {T})\le 7%$ if %$d(G)=3%$ and the bounds are sharp; (b) %$4\le n(G_\text {T})\le 9%$ if %$d(G)=2%$. Resolving set (dpeaa)DE-He213 Metric dimension (dpeaa)DE-He213 Extremal graph (dpeaa)DE-He213 Metric matrix (dpeaa)DE-He213 Tian, Fenglei aut Liu, Yunlong aut Pang, Jingru aut Miao, Lianying aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 2 vom: 06. März (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:2 day:06 month:03 https://dx.doi.org/10.1007/s00373-023-02627-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 2 06 03 |
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Enthalten in Graphs and combinatorics 39(2023), 2 vom: 06. März volume:39 year:2023 number:2 day:06 month:03 |
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Wang, Juan @@aut@@ Tian, Fenglei @@aut@@ Liu, Yunlong @@aut@@ Pang, Jingru @@aut@@ Miao, Lianying @@aut@@ |
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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">SPR049558188</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230510064745.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230307s2023 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00373-023-02627-x</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR049558188</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00373-023-02627-x-e</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="100" ind1="1" ind2=" "><subfield code="a">Wang, Juan</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0002-9937-7590</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On Graphs of Order n with Metric Dimension %$n-4%$</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2023</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">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract For a connected graph G, let n(G), d(G) and dim(G) denote the order, the diameter and the metric dimension of G, respectively. The twin graph %$G_\text {T}%$ is obtained from G by contracting each maximal set of vertices with the same open or close neighborhood into a vertex, respectively. In this paper, we propose a necessary and sufficient condition obtaining G from %$G_\text {T}%$ and characterize all graphs with dim%$(G)=n-4%$ and %$n(G_\text {T})=4%$ by this condition. For the graphs with dim%$(G)=n-4%$, we show the following results: (a) %$4\le n(G_\text {T})\le 7%$ if %$d(G)=3%$ and the bounds are sharp; (b) %$4\le n(G_\text {T})\le 9%$ if %$d(G)=2%$.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Resolving set</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Metric dimension</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Extremal graph</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Metric matrix</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Tian, Fenglei</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Liu, Yunlong</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Pang, Jingru</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Miao, Lianying</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Graphs and combinatorics</subfield><subfield code="d">Tokyo : Springer-Verl. Tokyo, 1985</subfield><subfield code="g">39(2023), 2 vom: 06. 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Wang, Juan |
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Wang, Juan misc Resolving set misc Metric dimension misc Extremal graph misc Metric matrix On Graphs of Order n with Metric Dimension %$n-4%$ |
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On Graphs of Order n with Metric Dimension %$n-4%$ Resolving set (dpeaa)DE-He213 Metric dimension (dpeaa)DE-He213 Extremal graph (dpeaa)DE-He213 Metric matrix (dpeaa)DE-He213 |
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on graphs of order n with metric dimension %$n-4%$ |
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On Graphs of Order n with Metric Dimension %$n-4%$ |
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Abstract For a connected graph G, let n(G), d(G) and dim(G) denote the order, the diameter and the metric dimension of G, respectively. The twin graph %$G_\text {T}%$ is obtained from G by contracting each maximal set of vertices with the same open or close neighborhood into a vertex, respectively. In this paper, we propose a necessary and sufficient condition obtaining G from %$G_\text {T}%$ and characterize all graphs with dim%$(G)=n-4%$ and %$n(G_\text {T})=4%$ by this condition. For the graphs with dim%$(G)=n-4%$, we show the following results: (a) %$4\le n(G_\text {T})\le 7%$ if %$d(G)=3%$ and the bounds are sharp; (b) %$4\le n(G_\text {T})\le 9%$ if %$d(G)=2%$. © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
abstractGer |
Abstract For a connected graph G, let n(G), d(G) and dim(G) denote the order, the diameter and the metric dimension of G, respectively. The twin graph %$G_\text {T}%$ is obtained from G by contracting each maximal set of vertices with the same open or close neighborhood into a vertex, respectively. In this paper, we propose a necessary and sufficient condition obtaining G from %$G_\text {T}%$ and characterize all graphs with dim%$(G)=n-4%$ and %$n(G_\text {T})=4%$ by this condition. For the graphs with dim%$(G)=n-4%$, we show the following results: (a) %$4\le n(G_\text {T})\le 7%$ if %$d(G)=3%$ and the bounds are sharp; (b) %$4\le n(G_\text {T})\le 9%$ if %$d(G)=2%$. © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
abstract_unstemmed |
Abstract For a connected graph G, let n(G), d(G) and dim(G) denote the order, the diameter and the metric dimension of G, respectively. The twin graph %$G_\text {T}%$ is obtained from G by contracting each maximal set of vertices with the same open or close neighborhood into a vertex, respectively. In this paper, we propose a necessary and sufficient condition obtaining G from %$G_\text {T}%$ and characterize all graphs with dim%$(G)=n-4%$ and %$n(G_\text {T})=4%$ by this condition. For the graphs with dim%$(G)=n-4%$, we show the following results: (a) %$4\le n(G_\text {T})\le 7%$ if %$d(G)=3%$ and the bounds are sharp; (b) %$4\le n(G_\text {T})\le 9%$ if %$d(G)=2%$. © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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container_issue |
2 |
title_short |
On Graphs of Order n with Metric Dimension %$n-4%$ |
url |
https://dx.doi.org/10.1007/s00373-023-02627-x |
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author2 |
Tian, Fenglei Liu, Yunlong Pang, Jingru Miao, Lianying |
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Tian, Fenglei Liu, Yunlong Pang, Jingru Miao, Lianying |
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doi_str |
10.1007/s00373-023-02627-x |
up_date |
2024-07-04T01:18:39.758Z |
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|
score |
7.400591 |