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

Gespeichert in:

Autor*in:	Wang, Juan [verfasserIn] Tian, Fenglei Liu, Yunlong Pang, Jingru Miao, Lianying

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Resolving set Metric dimension Extremal graph Metric matrix

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.

Übergeordnetes Werk:	Enthalten in: Graphs and combinatorics - Tokyo : Springer-Verl. Tokyo, 1985, 39(2023), 2 vom: 06. März
Übergeordnetes Werk:	volume:39 ; year:2023 ; number:2 ; day:06 ; month:03

Links:	Volltext

DOI / URN:	10.1007/s00373-023-02627-x

Katalog-ID:	SPR049558188

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100	1		\|a Wang, Juan \|e verfasserin \|0 (orcid)0000-0002-9937-7590 \|4 aut
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
773	1	8	\|g volume:39 \|g year:2023 \|g number:2 \|g day:06 \|g month:03
856	4	0	\|u https://dx.doi.org/10.1007/s00373-023-02627-x \|z lizenzpflichtig \|3 Volltext
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912			\|a GBV_ILN_40
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912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_206
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4328
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
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allfields	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
spelling	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
allfields_unstemmed	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
allfieldsGer	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
language	English
source	Enthalten in Graphs and combinatorics 39(2023), 2 vom: 06. März volume:39 year:2023 number:2 day:06 month:03
sourceStr	Enthalten in Graphs and combinatorics 39(2023), 2 vom: 06. März volume:39 year:2023 number:2 day:06 month:03
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Resolving set Metric dimension Extremal graph Metric matrix
isfreeaccess_bool	false
container_title	Graphs and combinatorics
authorswithroles_txt_mv	Wang, Juan @@aut@@ Tian, Fenglei @@aut@@ Liu, Yunlong @@aut@@ Pang, Jingru @@aut@@ Miao, Lianying @@aut@@
publishDateDaySort_date	2023-03-06T00:00:00Z
hierarchy_top_id	30018381X
id	SPR049558188
language_de	englisch
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author	Wang, Juan
spellingShingle	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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topic_title	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
topic	misc Resolving set misc Metric dimension misc Extremal graph misc Metric matrix
topic_unstemmed	misc Resolving set misc Metric dimension misc Extremal graph misc Metric matrix
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format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	On Graphs of Order n with Metric Dimension %$n-4%$
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title_full	On Graphs of Order n with Metric Dimension %$n-4%$
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author_browse	Wang, Juan Tian, Fenglei Liu, Yunlong Pang, Jingru Miao, Lianying
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title_sort	on graphs of order n with metric dimension %$n-4%$
title_auth	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 %$n-4%$
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author2	Tian, Fenglei Liu, Yunlong Pang, Jingru Miao, Lianying
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score	7.400591

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On Graphs of Order n with Metric Dimension %$n-4%$

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