On metric dimension of permutation graphs
Abstract The metric dimension%$\dim (G)%$ of a graph %$G%$ is the minimum number of vertices such that every vertex of %$G%$ is uniquely determined by its vector of distances to the set of chosen vertices. Let %$G_1%$ and %$G_2%$ be disjoint copies of a graph %$G%$, and let %$\sigma : V(G_1) \righta...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Hallaway, Michael [verfasserIn] Kang, Cong X. [verfasserIn] Yi, Eunjeong [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Journal of combinatorial optimization - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997, 28(2013), 4 vom: 03. Jan., Seite 814-826 |
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| Übergeordnetes Werk: |
volume:28 ; year:2013 ; number:4 ; day:03 ; month:01 ; pages:814-826 |
| Links: |
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| DOI / URN: |
10.1007/s10878-012-9587-3 |
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| Katalog-ID: |
SPR014286262 |
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| 245 | 1 | 0 | |a On metric dimension of permutation graphs |
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| 520 | |a Abstract The metric dimension%$\dim (G)%$ of a graph %$G%$ is the minimum number of vertices such that every vertex of %$G%$ is uniquely determined by its vector of distances to the set of chosen vertices. Let %$G_1%$ and %$G_2%$ be disjoint copies of a graph %$G%$, and let %$\sigma : V(G_1) \rightarrow V(G_2)%$ be a permutation. Then, a permutation graph%$G_{\sigma }=(V, E)%$ has the vertex set %$V=V(G_1) \cup V(G_2)%$ and the edge set %$E=E(G_1) \cup E(G_2) \cup \{uv \mid v=\sigma (u)\}%$. We show that %$2 \le \dim (G_{\sigma }) \le n-1%$ for any connected graph %$G%$ of order %$n%$ at least %$3%$. We give examples showing that neither is there a function %$f%$ such that %$\dim (G)<f(\dim (G_{\sigma }))%$ for all pairs %$(G,\sigma )%$, nor is there a function %$g%$ such that %$g(\dim (G))>\dim (G_{\sigma })%$ for all pairs %$(G, \sigma )%$. Further, we characterize permutation graphs %$G_{\sigma }%$ satisfying %$\dim (G_{\sigma })=n-1%$ when %$G%$ is a complete %$k%$-partite graph, a cycle, or a path on %$n%$ vertices. | ||
| 650 | 4 | |a Metric dimension |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Permutation graph |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Complete |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a -partite graph |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Cycle |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Path |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Kang, Cong X. |e verfasserin |4 aut | |
| 700 | 1 | |a Yi, Eunjeong |e verfasserin |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Journal of combinatorial optimization |d Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 |g 28(2013), 4 vom: 03. Jan., Seite 814-826 |w (DE-627)313324085 |w (DE-600)2005418-X |x 1573-2886 |7 nnns |
| 773 | 1 | 8 | |g volume:28 |g year:2013 |g number:4 |g day:03 |g month:01 |g pages:814-826 |
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2013 |
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31.12 31.80 |
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2013 |
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10.1007/s10878-012-9587-3 doi (DE-627)SPR014286262 (SPR)s10878-012-9587-3-e DE-627 ger DE-627 rakwb eng 510 ASE 31.12 bkl 31.80 bkl Hallaway, Michael verfasserin aut On metric dimension of permutation graphs 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The metric dimension%$\dim (G)%$ of a graph %$G%$ is the minimum number of vertices such that every vertex of %$G%$ is uniquely determined by its vector of distances to the set of chosen vertices. Let %$G_1%$ and %$G_2%$ be disjoint copies of a graph %$G%$, and let %$\sigma : V(G_1) \rightarrow V(G_2)%$ be a permutation. Then, a permutation graph%$G_{\sigma }=(V, E)%$ has the vertex set %$V=V(G_1) \cup V(G_2)%$ and the edge set %$E=E(G_1) \cup E(G_2) \cup \{uv \mid v=\sigma (u)\}%$. We show that %$2 \le \dim (G_{\sigma }) \le n-1%$ for any connected graph %$G%$ of order %$n%$ at least %$3%$. We give examples showing that neither is there a function %$f%$ such that %$\dim (G)<f(\dim (G_{\sigma }))%$ for all pairs %$(G,\sigma )%$, nor is there a function %$g%$ such that %$g(\dim (G))>\dim (G_{\sigma })%$ for all pairs %$(G, \sigma )%$. Further, we characterize permutation graphs %$G_{\sigma }%$ satisfying %$\dim (G_{\sigma })=n-1%$ when %$G%$ is a complete %$k%$-partite graph, a cycle, or a path on %$n%$ vertices. Metric dimension (dpeaa)DE-He213 Permutation graph (dpeaa)DE-He213 Complete (dpeaa)DE-He213 -partite graph (dpeaa)DE-He213 Cycle (dpeaa)DE-He213 Path (dpeaa)DE-He213 Kang, Cong X. verfasserin aut Yi, Eunjeong verfasserin aut Enthalten in Journal of combinatorial optimization Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 28(2013), 4 vom: 03. Jan., Seite 814-826 (DE-627)313324085 (DE-600)2005418-X 1573-2886 nnns volume:28 year:2013 number:4 day:03 month:01 pages:814-826 https://dx.doi.org/10.1007/s10878-012-9587-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.12 ASE 31.80 ASE AR 28 2013 4 03 01 814-826 |
| spelling |
10.1007/s10878-012-9587-3 doi (DE-627)SPR014286262 (SPR)s10878-012-9587-3-e DE-627 ger DE-627 rakwb eng 510 ASE 31.12 bkl 31.80 bkl Hallaway, Michael verfasserin aut On metric dimension of permutation graphs 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The metric dimension%$\dim (G)%$ of a graph %$G%$ is the minimum number of vertices such that every vertex of %$G%$ is uniquely determined by its vector of distances to the set of chosen vertices. Let %$G_1%$ and %$G_2%$ be disjoint copies of a graph %$G%$, and let %$\sigma : V(G_1) \rightarrow V(G_2)%$ be a permutation. Then, a permutation graph%$G_{\sigma }=(V, E)%$ has the vertex set %$V=V(G_1) \cup V(G_2)%$ and the edge set %$E=E(G_1) \cup E(G_2) \cup \{uv \mid v=\sigma (u)\}%$. We show that %$2 \le \dim (G_{\sigma }) \le n-1%$ for any connected graph %$G%$ of order %$n%$ at least %$3%$. We give examples showing that neither is there a function %$f%$ such that %$\dim (G)<f(\dim (G_{\sigma }))%$ for all pairs %$(G,\sigma )%$, nor is there a function %$g%$ such that %$g(\dim (G))>\dim (G_{\sigma })%$ for all pairs %$(G, \sigma )%$. Further, we characterize permutation graphs %$G_{\sigma }%$ satisfying %$\dim (G_{\sigma })=n-1%$ when %$G%$ is a complete %$k%$-partite graph, a cycle, or a path on %$n%$ vertices. Metric dimension (dpeaa)DE-He213 Permutation graph (dpeaa)DE-He213 Complete (dpeaa)DE-He213 -partite graph (dpeaa)DE-He213 Cycle (dpeaa)DE-He213 Path (dpeaa)DE-He213 Kang, Cong X. verfasserin aut Yi, Eunjeong verfasserin aut Enthalten in Journal of combinatorial optimization Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 28(2013), 4 vom: 03. Jan., Seite 814-826 (DE-627)313324085 (DE-600)2005418-X 1573-2886 nnns volume:28 year:2013 number:4 day:03 month:01 pages:814-826 https://dx.doi.org/10.1007/s10878-012-9587-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.12 ASE 31.80 ASE AR 28 2013 4 03 01 814-826 |
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10.1007/s10878-012-9587-3 doi (DE-627)SPR014286262 (SPR)s10878-012-9587-3-e DE-627 ger DE-627 rakwb eng 510 ASE 31.12 bkl 31.80 bkl Hallaway, Michael verfasserin aut On metric dimension of permutation graphs 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The metric dimension%$\dim (G)%$ of a graph %$G%$ is the minimum number of vertices such that every vertex of %$G%$ is uniquely determined by its vector of distances to the set of chosen vertices. Let %$G_1%$ and %$G_2%$ be disjoint copies of a graph %$G%$, and let %$\sigma : V(G_1) \rightarrow V(G_2)%$ be a permutation. Then, a permutation graph%$G_{\sigma }=(V, E)%$ has the vertex set %$V=V(G_1) \cup V(G_2)%$ and the edge set %$E=E(G_1) \cup E(G_2) \cup \{uv \mid v=\sigma (u)\}%$. We show that %$2 \le \dim (G_{\sigma }) \le n-1%$ for any connected graph %$G%$ of order %$n%$ at least %$3%$. We give examples showing that neither is there a function %$f%$ such that %$\dim (G)<f(\dim (G_{\sigma }))%$ for all pairs %$(G,\sigma )%$, nor is there a function %$g%$ such that %$g(\dim (G))>\dim (G_{\sigma })%$ for all pairs %$(G, \sigma )%$. Further, we characterize permutation graphs %$G_{\sigma }%$ satisfying %$\dim (G_{\sigma })=n-1%$ when %$G%$ is a complete %$k%$-partite graph, a cycle, or a path on %$n%$ vertices. Metric dimension (dpeaa)DE-He213 Permutation graph (dpeaa)DE-He213 Complete (dpeaa)DE-He213 -partite graph (dpeaa)DE-He213 Cycle (dpeaa)DE-He213 Path (dpeaa)DE-He213 Kang, Cong X. verfasserin aut Yi, Eunjeong verfasserin aut Enthalten in Journal of combinatorial optimization Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 28(2013), 4 vom: 03. Jan., Seite 814-826 (DE-627)313324085 (DE-600)2005418-X 1573-2886 nnns volume:28 year:2013 number:4 day:03 month:01 pages:814-826 https://dx.doi.org/10.1007/s10878-012-9587-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.12 ASE 31.80 ASE AR 28 2013 4 03 01 814-826 |
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10.1007/s10878-012-9587-3 doi (DE-627)SPR014286262 (SPR)s10878-012-9587-3-e DE-627 ger DE-627 rakwb eng 510 ASE 31.12 bkl 31.80 bkl Hallaway, Michael verfasserin aut On metric dimension of permutation graphs 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The metric dimension%$\dim (G)%$ of a graph %$G%$ is the minimum number of vertices such that every vertex of %$G%$ is uniquely determined by its vector of distances to the set of chosen vertices. Let %$G_1%$ and %$G_2%$ be disjoint copies of a graph %$G%$, and let %$\sigma : V(G_1) \rightarrow V(G_2)%$ be a permutation. Then, a permutation graph%$G_{\sigma }=(V, E)%$ has the vertex set %$V=V(G_1) \cup V(G_2)%$ and the edge set %$E=E(G_1) \cup E(G_2) \cup \{uv \mid v=\sigma (u)\}%$. We show that %$2 \le \dim (G_{\sigma }) \le n-1%$ for any connected graph %$G%$ of order %$n%$ at least %$3%$. We give examples showing that neither is there a function %$f%$ such that %$\dim (G)<f(\dim (G_{\sigma }))%$ for all pairs %$(G,\sigma )%$, nor is there a function %$g%$ such that %$g(\dim (G))>\dim (G_{\sigma })%$ for all pairs %$(G, \sigma )%$. Further, we characterize permutation graphs %$G_{\sigma }%$ satisfying %$\dim (G_{\sigma })=n-1%$ when %$G%$ is a complete %$k%$-partite graph, a cycle, or a path on %$n%$ vertices. Metric dimension (dpeaa)DE-He213 Permutation graph (dpeaa)DE-He213 Complete (dpeaa)DE-He213 -partite graph (dpeaa)DE-He213 Cycle (dpeaa)DE-He213 Path (dpeaa)DE-He213 Kang, Cong X. verfasserin aut Yi, Eunjeong verfasserin aut Enthalten in Journal of combinatorial optimization Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 28(2013), 4 vom: 03. Jan., Seite 814-826 (DE-627)313324085 (DE-600)2005418-X 1573-2886 nnns volume:28 year:2013 number:4 day:03 month:01 pages:814-826 https://dx.doi.org/10.1007/s10878-012-9587-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.12 ASE 31.80 ASE AR 28 2013 4 03 01 814-826 |
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10.1007/s10878-012-9587-3 doi (DE-627)SPR014286262 (SPR)s10878-012-9587-3-e DE-627 ger DE-627 rakwb eng 510 ASE 31.12 bkl 31.80 bkl Hallaway, Michael verfasserin aut On metric dimension of permutation graphs 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The metric dimension%$\dim (G)%$ of a graph %$G%$ is the minimum number of vertices such that every vertex of %$G%$ is uniquely determined by its vector of distances to the set of chosen vertices. Let %$G_1%$ and %$G_2%$ be disjoint copies of a graph %$G%$, and let %$\sigma : V(G_1) \rightarrow V(G_2)%$ be a permutation. Then, a permutation graph%$G_{\sigma }=(V, E)%$ has the vertex set %$V=V(G_1) \cup V(G_2)%$ and the edge set %$E=E(G_1) \cup E(G_2) \cup \{uv \mid v=\sigma (u)\}%$. We show that %$2 \le \dim (G_{\sigma }) \le n-1%$ for any connected graph %$G%$ of order %$n%$ at least %$3%$. We give examples showing that neither is there a function %$f%$ such that %$\dim (G)<f(\dim (G_{\sigma }))%$ for all pairs %$(G,\sigma )%$, nor is there a function %$g%$ such that %$g(\dim (G))>\dim (G_{\sigma })%$ for all pairs %$(G, \sigma )%$. Further, we characterize permutation graphs %$G_{\sigma }%$ satisfying %$\dim (G_{\sigma })=n-1%$ when %$G%$ is a complete %$k%$-partite graph, a cycle, or a path on %$n%$ vertices. Metric dimension (dpeaa)DE-He213 Permutation graph (dpeaa)DE-He213 Complete (dpeaa)DE-He213 -partite graph (dpeaa)DE-He213 Cycle (dpeaa)DE-He213 Path (dpeaa)DE-He213 Kang, Cong X. verfasserin aut Yi, Eunjeong verfasserin aut Enthalten in Journal of combinatorial optimization Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 28(2013), 4 vom: 03. Jan., Seite 814-826 (DE-627)313324085 (DE-600)2005418-X 1573-2886 nnns volume:28 year:2013 number:4 day:03 month:01 pages:814-826 https://dx.doi.org/10.1007/s10878-012-9587-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.12 ASE 31.80 ASE AR 28 2013 4 03 01 814-826 |
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Enthalten in Journal of combinatorial optimization 28(2013), 4 vom: 03. Jan., Seite 814-826 volume:28 year:2013 number:4 day:03 month:01 pages:814-826 |
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Enthalten in Journal of combinatorial optimization 28(2013), 4 vom: 03. Jan., Seite 814-826 volume:28 year:2013 number:4 day:03 month:01 pages:814-826 |
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Hallaway, Michael @@aut@@ Kang, Cong X. @@aut@@ Yi, Eunjeong @@aut@@ |
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Let %$G_1%$ and %$G_2%$ be disjoint copies of a graph %$G%$, and let %$\sigma : V(G_1) \rightarrow V(G_2)%$ be a permutation. Then, a permutation graph%$G_{\sigma }=(V, E)%$ has the vertex set %$V=V(G_1) \cup V(G_2)%$ and the edge set %$E=E(G_1) \cup E(G_2) \cup \{uv \mid v=\sigma (u)\}%$. We show that %$2 \le \dim (G_{\sigma }) \le n-1%$ for any connected graph %$G%$ of order %$n%$ at least %$3%$. We give examples showing that neither is there a function %$f%$ such that %$\dim (G)<f(\dim (G_{\sigma }))%$ for all pairs %$(G,\sigma )%$, nor is there a function %$g%$ such that %$g(\dim (G))>\dim (G_{\sigma })%$ for all pairs %$(G, \sigma )%$. Further, we characterize permutation graphs %$G_{\sigma }%$ satisfying %$\dim (G_{\sigma })=n-1%$ when %$G%$ is a complete %$k%$-partite graph, a cycle, or a path on %$n%$ vertices.</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">Permutation graph</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Complete</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">-partite graph</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Cycle</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Path</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kang, Cong X.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Yi, Eunjeong</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of combinatorial optimization</subfield><subfield code="d">Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997</subfield><subfield code="g">28(2013), 4 vom: 03. 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Hallaway, Michael |
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Hallaway, Michael ddc 510 bkl 31.12 bkl 31.80 misc Metric dimension misc Permutation graph misc Complete misc -partite graph misc Cycle misc Path On metric dimension of permutation graphs |
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510 ASE 31.12 bkl 31.80 bkl On metric dimension of permutation graphs Metric dimension (dpeaa)DE-He213 Permutation graph (dpeaa)DE-He213 Complete (dpeaa)DE-He213 -partite graph (dpeaa)DE-He213 Cycle (dpeaa)DE-He213 Path (dpeaa)DE-He213 |
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ddc 510 bkl 31.12 bkl 31.80 misc Metric dimension misc Permutation graph misc Complete misc -partite graph misc Cycle misc Path |
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on metric dimension of permutation graphs |
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On metric dimension of permutation graphs |
| abstract |
Abstract The metric dimension%$\dim (G)%$ of a graph %$G%$ is the minimum number of vertices such that every vertex of %$G%$ is uniquely determined by its vector of distances to the set of chosen vertices. Let %$G_1%$ and %$G_2%$ be disjoint copies of a graph %$G%$, and let %$\sigma : V(G_1) \rightarrow V(G_2)%$ be a permutation. Then, a permutation graph%$G_{\sigma }=(V, E)%$ has the vertex set %$V=V(G_1) \cup V(G_2)%$ and the edge set %$E=E(G_1) \cup E(G_2) \cup \{uv \mid v=\sigma (u)\}%$. We show that %$2 \le \dim (G_{\sigma }) \le n-1%$ for any connected graph %$G%$ of order %$n%$ at least %$3%$. We give examples showing that neither is there a function %$f%$ such that %$\dim (G)<f(\dim (G_{\sigma }))%$ for all pairs %$(G,\sigma )%$, nor is there a function %$g%$ such that %$g(\dim (G))>\dim (G_{\sigma })%$ for all pairs %$(G, \sigma )%$. Further, we characterize permutation graphs %$G_{\sigma }%$ satisfying %$\dim (G_{\sigma })=n-1%$ when %$G%$ is a complete %$k%$-partite graph, a cycle, or a path on %$n%$ vertices. |
| abstractGer |
Abstract The metric dimension%$\dim (G)%$ of a graph %$G%$ is the minimum number of vertices such that every vertex of %$G%$ is uniquely determined by its vector of distances to the set of chosen vertices. Let %$G_1%$ and %$G_2%$ be disjoint copies of a graph %$G%$, and let %$\sigma : V(G_1) \rightarrow V(G_2)%$ be a permutation. Then, a permutation graph%$G_{\sigma }=(V, E)%$ has the vertex set %$V=V(G_1) \cup V(G_2)%$ and the edge set %$E=E(G_1) \cup E(G_2) \cup \{uv \mid v=\sigma (u)\}%$. We show that %$2 \le \dim (G_{\sigma }) \le n-1%$ for any connected graph %$G%$ of order %$n%$ at least %$3%$. We give examples showing that neither is there a function %$f%$ such that %$\dim (G)<f(\dim (G_{\sigma }))%$ for all pairs %$(G,\sigma )%$, nor is there a function %$g%$ such that %$g(\dim (G))>\dim (G_{\sigma })%$ for all pairs %$(G, \sigma )%$. Further, we characterize permutation graphs %$G_{\sigma }%$ satisfying %$\dim (G_{\sigma })=n-1%$ when %$G%$ is a complete %$k%$-partite graph, a cycle, or a path on %$n%$ vertices. |
| abstract_unstemmed |
Abstract The metric dimension%$\dim (G)%$ of a graph %$G%$ is the minimum number of vertices such that every vertex of %$G%$ is uniquely determined by its vector of distances to the set of chosen vertices. Let %$G_1%$ and %$G_2%$ be disjoint copies of a graph %$G%$, and let %$\sigma : V(G_1) \rightarrow V(G_2)%$ be a permutation. Then, a permutation graph%$G_{\sigma }=(V, E)%$ has the vertex set %$V=V(G_1) \cup V(G_2)%$ and the edge set %$E=E(G_1) \cup E(G_2) \cup \{uv \mid v=\sigma (u)\}%$. We show that %$2 \le \dim (G_{\sigma }) \le n-1%$ for any connected graph %$G%$ of order %$n%$ at least %$3%$. We give examples showing that neither is there a function %$f%$ such that %$\dim (G)<f(\dim (G_{\sigma }))%$ for all pairs %$(G,\sigma )%$, nor is there a function %$g%$ such that %$g(\dim (G))>\dim (G_{\sigma })%$ for all pairs %$(G, \sigma )%$. Further, we characterize permutation graphs %$G_{\sigma }%$ satisfying %$\dim (G_{\sigma })=n-1%$ when %$G%$ is a complete %$k%$-partite graph, a cycle, or a path on %$n%$ vertices. |
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| title_short |
On metric dimension of permutation graphs |
| url |
https://dx.doi.org/10.1007/s10878-012-9587-3 |
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| author2 |
Kang, Cong X. Yi, Eunjeong |
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Kang, Cong X. Yi, Eunjeong |
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| doi_str |
10.1007/s10878-012-9587-3 |
| up_date |
2024-07-04T01:02:10.344Z |
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| score |
7.3996363 |