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: |
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 - Springer Japan, 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: |
OLC2134315245 |
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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 $$d(G)=2$$. | ||
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700 | 1 | |a Pang, Jingru |4 aut | |
700 | 1 | |a Miao, Lianying |4 aut | |
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10.1007/s00373-023-02627-x doi (DE-627)OLC2134315245 (DE-He213)s00373-023-02627-x-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Wang, Juan verfasserin (orcid)0000-0002-9937-7590 aut On Graphs of Order n with Metric Dimension $$n-4$$ 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc 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 Metric dimension Extremal graph Metric matrix Tian, Fenglei aut Liu, Yunlong aut Pang, Jingru aut Miao, Lianying aut Enthalten in Graphs and combinatorics Springer Japan, 1985 39(2023), 2 vom: 06. März (DE-627)129274453 (DE-600)84314-3 (DE-576)014463903 0911-0119 nnns volume:39 year:2023 number:2 day:06 month:03 https://doi.org/10.1007/s00373-023-02627-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 39 2023 2 06 03 |
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10.1007/s00373-023-02627-x doi (DE-627)OLC2134315245 (DE-He213)s00373-023-02627-x-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Wang, Juan verfasserin (orcid)0000-0002-9937-7590 aut On Graphs of Order n with Metric Dimension $$n-4$$ 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc 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 Metric dimension Extremal graph Metric matrix Tian, Fenglei aut Liu, Yunlong aut Pang, Jingru aut Miao, Lianying aut Enthalten in Graphs and combinatorics Springer Japan, 1985 39(2023), 2 vom: 06. März (DE-627)129274453 (DE-600)84314-3 (DE-576)014463903 0911-0119 nnns volume:39 year:2023 number:2 day:06 month:03 https://doi.org/10.1007/s00373-023-02627-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 39 2023 2 06 03 |
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10.1007/s00373-023-02627-x doi (DE-627)OLC2134315245 (DE-He213)s00373-023-02627-x-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Wang, Juan verfasserin (orcid)0000-0002-9937-7590 aut On Graphs of Order n with Metric Dimension $$n-4$$ 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc 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 Metric dimension Extremal graph Metric matrix Tian, Fenglei aut Liu, Yunlong aut Pang, Jingru aut Miao, Lianying aut Enthalten in Graphs and combinatorics Springer Japan, 1985 39(2023), 2 vom: 06. März (DE-627)129274453 (DE-600)84314-3 (DE-576)014463903 0911-0119 nnns volume:39 year:2023 number:2 day:06 month:03 https://doi.org/10.1007/s00373-023-02627-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 39 2023 2 06 03 |
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10.1007/s00373-023-02627-x doi (DE-627)OLC2134315245 (DE-He213)s00373-023-02627-x-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Wang, Juan verfasserin (orcid)0000-0002-9937-7590 aut On Graphs of Order n with Metric Dimension $$n-4$$ 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc 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 Metric dimension Extremal graph Metric matrix Tian, Fenglei aut Liu, Yunlong aut Pang, Jingru aut Miao, Lianying aut Enthalten in Graphs and combinatorics Springer Japan, 1985 39(2023), 2 vom: 06. März (DE-627)129274453 (DE-600)84314-3 (DE-576)014463903 0911-0119 nnns volume:39 year:2023 number:2 day:06 month:03 https://doi.org/10.1007/s00373-023-02627-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 39 2023 2 06 03 |
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10.1007/s00373-023-02627-x doi (DE-627)OLC2134315245 (DE-He213)s00373-023-02627-x-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Wang, Juan verfasserin (orcid)0000-0002-9937-7590 aut On Graphs of Order n with Metric Dimension $$n-4$$ 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc 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 Metric dimension Extremal graph Metric matrix Tian, Fenglei aut Liu, Yunlong aut Pang, Jingru aut Miao, Lianying aut Enthalten in Graphs and combinatorics Springer Japan, 1985 39(2023), 2 vom: 06. März (DE-627)129274453 (DE-600)84314-3 (DE-576)014463903 0911-0119 nnns volume:39 year:2023 number:2 day:06 month:03 https://doi.org/10.1007/s00373-023-02627-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 39 2023 2 06 03 |
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On Graphs of Order n with Metric Dimension $$n-4$$ |
abstract |
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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title_short |
On Graphs of Order n with Metric Dimension $$n-4$$ |
url |
https://doi.org/10.1007/s00373-023-02627-x |
remote_bool |
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author2 |
Tian, Fenglei Liu, Yunlong Pang, Jingru Miao, Lianying |
author2Str |
Tian, Fenglei Liu, Yunlong Pang, Jingru Miao, Lianying |
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129274453 |
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doi_str |
10.1007/s00373-023-02627-x |
up_date |
2024-07-04T00:32:50.043Z |
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