An Introduction to Closed/Open Neighborhood Sums: Minimax, Maximin, and Spread
Abstract For a graph G of order |V(G)| = n and a real-valued mapping %${f:V(G)\rightarrow\mathbb{R}}%$, if %${S\subset V(G)}%$ then %${f(S)=\sum_{w\in S} f(w)}%$ is called the weight of S under f. The closed (respectively, open) neighborhood sum of f is the maximum weight of a closed (respectively,...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
O’Neal, Allen [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2011 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Basel AG 2011 |
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| Übergeordnetes Werk: |
Enthalten in: Mathematics in computer science - Cham (ZG) : Springer International Publishing AG, 2007, 5(2011), 1 vom: März, Seite 69-80 |
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| Übergeordnetes Werk: |
volume:5 ; year:2011 ; number:1 ; month:03 ; pages:69-80 |
| Links: |
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| DOI / URN: |
10.1007/s11786-011-0075-4 |
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| Katalog-ID: |
SPR022423869 |
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| 041 | |a eng | ||
| 100 | 1 | |a O’Neal, Allen |e verfasserin |4 aut | |
| 245 | 1 | 3 | |a An Introduction to Closed/Open Neighborhood Sums: Minimax, Maximin, and Spread |
| 264 | 1 | |c 2011 | |
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| 337 | |a Computermedien |b c |2 rdamedia | ||
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| 500 | |a © Springer Basel AG 2011 | ||
| 520 | |a Abstract For a graph G of order |V(G)| = n and a real-valued mapping %${f:V(G)\rightarrow\mathbb{R}}%$, if %${S\subset V(G)}%$ then %${f(S)=\sum_{w\in S} f(w)}%$ is called the weight of S under f. The closed (respectively, open) neighborhood sum of f is the maximum weight of a closed (respectively, open) neighborhood under f, that is, %${NS[f]={\rm max}\{f(N[v])|v \in V(G)\}}%$ and %${NS(f)={\rm max}\{f(N(v))|v \in V(G)\}}%$. The closed (respectively, open) lower neighborhood sum of f is the minimum weight of a closed (respectively, open) neighborhood under f, that is, %${NS^{-}[f]={\rm min}\{f(N[v])|v\in V(G)\}}%$ and %${NS^{-}(f)={\rm min}\{f(N(v))|v\in V(G)\}}%$. For %${W\subset \mathbb{R}}%$, the closed and open neighborhood sum parameters are %${NS_W[G]={\rm min}\{NS[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS_W(G)={\rm min}\{NS(f)|f:V(G)\rightarrow W}%$ is a bijection}. The lower neighbor sum parameters are %${NS^{-}_W[G]={\rm max}NS^{-}[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS^{-}_W(G)={\rm max}NS^{-}(f)|f:V(G)\rightarrow W}%$ is a bijection}. For bijections %${f:V(G)\rightarrow \{1,2,\ldots,n\}}%$ we consider the parameters NS[G], NS(G), NS−[G] and NS−(G), as well as two parameters minimizing the maximum difference in neighborhood sums. | ||
| 650 | 4 | |a Graph labeling |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Sigma labeling |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Neighborhood sums |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Slater, Peter J. |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Mathematics in computer science |d Cham (ZG) : Springer International Publishing AG, 2007 |g 5(2011), 1 vom: März, Seite 69-80 |w (DE-627)548639310 |w (DE-600)2394773-1 |x 1661-8289 |7 nnns |
| 773 | 1 | 8 | |g volume:5 |g year:2011 |g number:1 |g month:03 |g pages:69-80 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s11786-011-0075-4 |z lizenzpflichtig |3 Volltext |
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| 952 | |d 5 |j 2011 |e 1 |c 03 |h 69-80 | ||
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10.1007/s11786-011-0075-4 doi (DE-627)SPR022423869 (SPR)s11786-011-0075-4-e DE-627 ger DE-627 rakwb eng O’Neal, Allen verfasserin aut An Introduction to Closed/Open Neighborhood Sums: Minimax, Maximin, and Spread 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel AG 2011 Abstract For a graph G of order |V(G)| = n and a real-valued mapping %${f:V(G)\rightarrow\mathbb{R}}%$, if %${S\subset V(G)}%$ then %${f(S)=\sum_{w\in S} f(w)}%$ is called the weight of S under f. The closed (respectively, open) neighborhood sum of f is the maximum weight of a closed (respectively, open) neighborhood under f, that is, %${NS[f]={\rm max}\{f(N[v])|v \in V(G)\}}%$ and %${NS(f)={\rm max}\{f(N(v))|v \in V(G)\}}%$. The closed (respectively, open) lower neighborhood sum of f is the minimum weight of a closed (respectively, open) neighborhood under f, that is, %${NS^{-}[f]={\rm min}\{f(N[v])|v\in V(G)\}}%$ and %${NS^{-}(f)={\rm min}\{f(N(v))|v\in V(G)\}}%$. For %${W\subset \mathbb{R}}%$, the closed and open neighborhood sum parameters are %${NS_W[G]={\rm min}\{NS[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS_W(G)={\rm min}\{NS(f)|f:V(G)\rightarrow W}%$ is a bijection}. The lower neighbor sum parameters are %${NS^{-}_W[G]={\rm max}NS^{-}[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS^{-}_W(G)={\rm max}NS^{-}(f)|f:V(G)\rightarrow W}%$ is a bijection}. For bijections %${f:V(G)\rightarrow \{1,2,\ldots,n\}}%$ we consider the parameters NS[G], NS(G), NS−[G] and NS−(G), as well as two parameters minimizing the maximum difference in neighborhood sums. Graph labeling (dpeaa)DE-He213 Sigma labeling (dpeaa)DE-He213 Neighborhood sums (dpeaa)DE-He213 Slater, Peter J. aut Enthalten in Mathematics in computer science Cham (ZG) : Springer International Publishing AG, 2007 5(2011), 1 vom: März, Seite 69-80 (DE-627)548639310 (DE-600)2394773-1 1661-8289 nnns volume:5 year:2011 number:1 month:03 pages:69-80 https://dx.doi.org/10.1007/s11786-011-0075-4 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 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 AR 5 2011 1 03 69-80 |
| spelling |
10.1007/s11786-011-0075-4 doi (DE-627)SPR022423869 (SPR)s11786-011-0075-4-e DE-627 ger DE-627 rakwb eng O’Neal, Allen verfasserin aut An Introduction to Closed/Open Neighborhood Sums: Minimax, Maximin, and Spread 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel AG 2011 Abstract For a graph G of order |V(G)| = n and a real-valued mapping %${f:V(G)\rightarrow\mathbb{R}}%$, if %${S\subset V(G)}%$ then %${f(S)=\sum_{w\in S} f(w)}%$ is called the weight of S under f. The closed (respectively, open) neighborhood sum of f is the maximum weight of a closed (respectively, open) neighborhood under f, that is, %${NS[f]={\rm max}\{f(N[v])|v \in V(G)\}}%$ and %${NS(f)={\rm max}\{f(N(v))|v \in V(G)\}}%$. The closed (respectively, open) lower neighborhood sum of f is the minimum weight of a closed (respectively, open) neighborhood under f, that is, %${NS^{-}[f]={\rm min}\{f(N[v])|v\in V(G)\}}%$ and %${NS^{-}(f)={\rm min}\{f(N(v))|v\in V(G)\}}%$. For %${W\subset \mathbb{R}}%$, the closed and open neighborhood sum parameters are %${NS_W[G]={\rm min}\{NS[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS_W(G)={\rm min}\{NS(f)|f:V(G)\rightarrow W}%$ is a bijection}. The lower neighbor sum parameters are %${NS^{-}_W[G]={\rm max}NS^{-}[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS^{-}_W(G)={\rm max}NS^{-}(f)|f:V(G)\rightarrow W}%$ is a bijection}. For bijections %${f:V(G)\rightarrow \{1,2,\ldots,n\}}%$ we consider the parameters NS[G], NS(G), NS−[G] and NS−(G), as well as two parameters minimizing the maximum difference in neighborhood sums. Graph labeling (dpeaa)DE-He213 Sigma labeling (dpeaa)DE-He213 Neighborhood sums (dpeaa)DE-He213 Slater, Peter J. aut Enthalten in Mathematics in computer science Cham (ZG) : Springer International Publishing AG, 2007 5(2011), 1 vom: März, Seite 69-80 (DE-627)548639310 (DE-600)2394773-1 1661-8289 nnns volume:5 year:2011 number:1 month:03 pages:69-80 https://dx.doi.org/10.1007/s11786-011-0075-4 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 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 AR 5 2011 1 03 69-80 |
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10.1007/s11786-011-0075-4 doi (DE-627)SPR022423869 (SPR)s11786-011-0075-4-e DE-627 ger DE-627 rakwb eng O’Neal, Allen verfasserin aut An Introduction to Closed/Open Neighborhood Sums: Minimax, Maximin, and Spread 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel AG 2011 Abstract For a graph G of order |V(G)| = n and a real-valued mapping %${f:V(G)\rightarrow\mathbb{R}}%$, if %${S\subset V(G)}%$ then %${f(S)=\sum_{w\in S} f(w)}%$ is called the weight of S under f. The closed (respectively, open) neighborhood sum of f is the maximum weight of a closed (respectively, open) neighborhood under f, that is, %${NS[f]={\rm max}\{f(N[v])|v \in V(G)\}}%$ and %${NS(f)={\rm max}\{f(N(v))|v \in V(G)\}}%$. The closed (respectively, open) lower neighborhood sum of f is the minimum weight of a closed (respectively, open) neighborhood under f, that is, %${NS^{-}[f]={\rm min}\{f(N[v])|v\in V(G)\}}%$ and %${NS^{-}(f)={\rm min}\{f(N(v))|v\in V(G)\}}%$. For %${W\subset \mathbb{R}}%$, the closed and open neighborhood sum parameters are %${NS_W[G]={\rm min}\{NS[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS_W(G)={\rm min}\{NS(f)|f:V(G)\rightarrow W}%$ is a bijection}. The lower neighbor sum parameters are %${NS^{-}_W[G]={\rm max}NS^{-}[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS^{-}_W(G)={\rm max}NS^{-}(f)|f:V(G)\rightarrow W}%$ is a bijection}. For bijections %${f:V(G)\rightarrow \{1,2,\ldots,n\}}%$ we consider the parameters NS[G], NS(G), NS−[G] and NS−(G), as well as two parameters minimizing the maximum difference in neighborhood sums. Graph labeling (dpeaa)DE-He213 Sigma labeling (dpeaa)DE-He213 Neighborhood sums (dpeaa)DE-He213 Slater, Peter J. aut Enthalten in Mathematics in computer science Cham (ZG) : Springer International Publishing AG, 2007 5(2011), 1 vom: März, Seite 69-80 (DE-627)548639310 (DE-600)2394773-1 1661-8289 nnns volume:5 year:2011 number:1 month:03 pages:69-80 https://dx.doi.org/10.1007/s11786-011-0075-4 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 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 AR 5 2011 1 03 69-80 |
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10.1007/s11786-011-0075-4 doi (DE-627)SPR022423869 (SPR)s11786-011-0075-4-e DE-627 ger DE-627 rakwb eng O’Neal, Allen verfasserin aut An Introduction to Closed/Open Neighborhood Sums: Minimax, Maximin, and Spread 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel AG 2011 Abstract For a graph G of order |V(G)| = n and a real-valued mapping %${f:V(G)\rightarrow\mathbb{R}}%$, if %${S\subset V(G)}%$ then %${f(S)=\sum_{w\in S} f(w)}%$ is called the weight of S under f. The closed (respectively, open) neighborhood sum of f is the maximum weight of a closed (respectively, open) neighborhood under f, that is, %${NS[f]={\rm max}\{f(N[v])|v \in V(G)\}}%$ and %${NS(f)={\rm max}\{f(N(v))|v \in V(G)\}}%$. The closed (respectively, open) lower neighborhood sum of f is the minimum weight of a closed (respectively, open) neighborhood under f, that is, %${NS^{-}[f]={\rm min}\{f(N[v])|v\in V(G)\}}%$ and %${NS^{-}(f)={\rm min}\{f(N(v))|v\in V(G)\}}%$. For %${W\subset \mathbb{R}}%$, the closed and open neighborhood sum parameters are %${NS_W[G]={\rm min}\{NS[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS_W(G)={\rm min}\{NS(f)|f:V(G)\rightarrow W}%$ is a bijection}. The lower neighbor sum parameters are %${NS^{-}_W[G]={\rm max}NS^{-}[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS^{-}_W(G)={\rm max}NS^{-}(f)|f:V(G)\rightarrow W}%$ is a bijection}. For bijections %${f:V(G)\rightarrow \{1,2,\ldots,n\}}%$ we consider the parameters NS[G], NS(G), NS−[G] and NS−(G), as well as two parameters minimizing the maximum difference in neighborhood sums. Graph labeling (dpeaa)DE-He213 Sigma labeling (dpeaa)DE-He213 Neighborhood sums (dpeaa)DE-He213 Slater, Peter J. aut Enthalten in Mathematics in computer science Cham (ZG) : Springer International Publishing AG, 2007 5(2011), 1 vom: März, Seite 69-80 (DE-627)548639310 (DE-600)2394773-1 1661-8289 nnns volume:5 year:2011 number:1 month:03 pages:69-80 https://dx.doi.org/10.1007/s11786-011-0075-4 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 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 AR 5 2011 1 03 69-80 |
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10.1007/s11786-011-0075-4 doi (DE-627)SPR022423869 (SPR)s11786-011-0075-4-e DE-627 ger DE-627 rakwb eng O’Neal, Allen verfasserin aut An Introduction to Closed/Open Neighborhood Sums: Minimax, Maximin, and Spread 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel AG 2011 Abstract For a graph G of order |V(G)| = n and a real-valued mapping %${f:V(G)\rightarrow\mathbb{R}}%$, if %${S\subset V(G)}%$ then %${f(S)=\sum_{w\in S} f(w)}%$ is called the weight of S under f. The closed (respectively, open) neighborhood sum of f is the maximum weight of a closed (respectively, open) neighborhood under f, that is, %${NS[f]={\rm max}\{f(N[v])|v \in V(G)\}}%$ and %${NS(f)={\rm max}\{f(N(v))|v \in V(G)\}}%$. The closed (respectively, open) lower neighborhood sum of f is the minimum weight of a closed (respectively, open) neighborhood under f, that is, %${NS^{-}[f]={\rm min}\{f(N[v])|v\in V(G)\}}%$ and %${NS^{-}(f)={\rm min}\{f(N(v))|v\in V(G)\}}%$. For %${W\subset \mathbb{R}}%$, the closed and open neighborhood sum parameters are %${NS_W[G]={\rm min}\{NS[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS_W(G)={\rm min}\{NS(f)|f:V(G)\rightarrow W}%$ is a bijection}. The lower neighbor sum parameters are %${NS^{-}_W[G]={\rm max}NS^{-}[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS^{-}_W(G)={\rm max}NS^{-}(f)|f:V(G)\rightarrow W}%$ is a bijection}. For bijections %${f:V(G)\rightarrow \{1,2,\ldots,n\}}%$ we consider the parameters NS[G], NS(G), NS−[G] and NS−(G), as well as two parameters minimizing the maximum difference in neighborhood sums. Graph labeling (dpeaa)DE-He213 Sigma labeling (dpeaa)DE-He213 Neighborhood sums (dpeaa)DE-He213 Slater, Peter J. aut Enthalten in Mathematics in computer science Cham (ZG) : Springer International Publishing AG, 2007 5(2011), 1 vom: März, Seite 69-80 (DE-627)548639310 (DE-600)2394773-1 1661-8289 nnns volume:5 year:2011 number:1 month:03 pages:69-80 https://dx.doi.org/10.1007/s11786-011-0075-4 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 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 AR 5 2011 1 03 69-80 |
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Enthalten in Mathematics in computer science 5(2011), 1 vom: März, Seite 69-80 volume:5 year:2011 number:1 month:03 pages:69-80 |
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The closed (respectively, open) neighborhood sum of f is the maximum weight of a closed (respectively, open) neighborhood under f, that is, %${NS[f]={\rm max}\{f(N[v])|v \in V(G)\}}%$ and %${NS(f)={\rm max}\{f(N(v))|v \in V(G)\}}%$. The closed (respectively, open) lower neighborhood sum of f is the minimum weight of a closed (respectively, open) neighborhood under f, that is, %${NS^{-}[f]={\rm min}\{f(N[v])|v\in V(G)\}}%$ and %${NS^{-}(f)={\rm min}\{f(N(v))|v\in V(G)\}}%$. For %${W\subset \mathbb{R}}%$, the closed and open neighborhood sum parameters are %${NS_W[G]={\rm min}\{NS[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS_W(G)={\rm min}\{NS(f)|f:V(G)\rightarrow W}%$ is a bijection}. The lower neighbor sum parameters are %${NS^{-}_W[G]={\rm max}NS^{-}[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS^{-}_W(G)={\rm max}NS^{-}(f)|f:V(G)\rightarrow W}%$ is a bijection}. For bijections %${f:V(G)\rightarrow \{1,2,\ldots,n\}}%$ we consider the parameters NS[G], NS(G), NS−[G] and NS−(G), as well as two parameters minimizing the maximum difference in neighborhood sums.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Graph labeling</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sigma labeling</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Neighborhood sums</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Slater, Peter J.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Mathematics in computer science</subfield><subfield code="d">Cham (ZG) : Springer International Publishing AG, 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An Introduction to Closed/Open Neighborhood Sums: Minimax, Maximin, and Spread Graph labeling (dpeaa)DE-He213 Sigma labeling (dpeaa)DE-He213 Neighborhood sums (dpeaa)DE-He213 |
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introduction to closed/open neighborhood sums: minimax, maximin, and spread |
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An Introduction to Closed/Open Neighborhood Sums: Minimax, Maximin, and Spread |
| abstract |
Abstract For a graph G of order |V(G)| = n and a real-valued mapping %${f:V(G)\rightarrow\mathbb{R}}%$, if %${S\subset V(G)}%$ then %${f(S)=\sum_{w\in S} f(w)}%$ is called the weight of S under f. The closed (respectively, open) neighborhood sum of f is the maximum weight of a closed (respectively, open) neighborhood under f, that is, %${NS[f]={\rm max}\{f(N[v])|v \in V(G)\}}%$ and %${NS(f)={\rm max}\{f(N(v))|v \in V(G)\}}%$. The closed (respectively, open) lower neighborhood sum of f is the minimum weight of a closed (respectively, open) neighborhood under f, that is, %${NS^{-}[f]={\rm min}\{f(N[v])|v\in V(G)\}}%$ and %${NS^{-}(f)={\rm min}\{f(N(v))|v\in V(G)\}}%$. For %${W\subset \mathbb{R}}%$, the closed and open neighborhood sum parameters are %${NS_W[G]={\rm min}\{NS[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS_W(G)={\rm min}\{NS(f)|f:V(G)\rightarrow W}%$ is a bijection}. The lower neighbor sum parameters are %${NS^{-}_W[G]={\rm max}NS^{-}[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS^{-}_W(G)={\rm max}NS^{-}(f)|f:V(G)\rightarrow W}%$ is a bijection}. For bijections %${f:V(G)\rightarrow \{1,2,\ldots,n\}}%$ we consider the parameters NS[G], NS(G), NS−[G] and NS−(G), as well as two parameters minimizing the maximum difference in neighborhood sums. © Springer Basel AG 2011 |
| abstractGer |
Abstract For a graph G of order |V(G)| = n and a real-valued mapping %${f:V(G)\rightarrow\mathbb{R}}%$, if %${S\subset V(G)}%$ then %${f(S)=\sum_{w\in S} f(w)}%$ is called the weight of S under f. The closed (respectively, open) neighborhood sum of f is the maximum weight of a closed (respectively, open) neighborhood under f, that is, %${NS[f]={\rm max}\{f(N[v])|v \in V(G)\}}%$ and %${NS(f)={\rm max}\{f(N(v))|v \in V(G)\}}%$. The closed (respectively, open) lower neighborhood sum of f is the minimum weight of a closed (respectively, open) neighborhood under f, that is, %${NS^{-}[f]={\rm min}\{f(N[v])|v\in V(G)\}}%$ and %${NS^{-}(f)={\rm min}\{f(N(v))|v\in V(G)\}}%$. For %${W\subset \mathbb{R}}%$, the closed and open neighborhood sum parameters are %${NS_W[G]={\rm min}\{NS[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS_W(G)={\rm min}\{NS(f)|f:V(G)\rightarrow W}%$ is a bijection}. The lower neighbor sum parameters are %${NS^{-}_W[G]={\rm max}NS^{-}[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS^{-}_W(G)={\rm max}NS^{-}(f)|f:V(G)\rightarrow W}%$ is a bijection}. For bijections %${f:V(G)\rightarrow \{1,2,\ldots,n\}}%$ we consider the parameters NS[G], NS(G), NS−[G] and NS−(G), as well as two parameters minimizing the maximum difference in neighborhood sums. © Springer Basel AG 2011 |
| abstract_unstemmed |
Abstract For a graph G of order |V(G)| = n and a real-valued mapping %${f:V(G)\rightarrow\mathbb{R}}%$, if %${S\subset V(G)}%$ then %${f(S)=\sum_{w\in S} f(w)}%$ is called the weight of S under f. The closed (respectively, open) neighborhood sum of f is the maximum weight of a closed (respectively, open) neighborhood under f, that is, %${NS[f]={\rm max}\{f(N[v])|v \in V(G)\}}%$ and %${NS(f)={\rm max}\{f(N(v))|v \in V(G)\}}%$. The closed (respectively, open) lower neighborhood sum of f is the minimum weight of a closed (respectively, open) neighborhood under f, that is, %${NS^{-}[f]={\rm min}\{f(N[v])|v\in V(G)\}}%$ and %${NS^{-}(f)={\rm min}\{f(N(v))|v\in V(G)\}}%$. For %${W\subset \mathbb{R}}%$, the closed and open neighborhood sum parameters are %${NS_W[G]={\rm min}\{NS[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS_W(G)={\rm min}\{NS(f)|f:V(G)\rightarrow W}%$ is a bijection}. The lower neighbor sum parameters are %${NS^{-}_W[G]={\rm max}NS^{-}[f]|f:V(G)\rightarrow W}%$ is a bijection} and %${NS^{-}_W(G)={\rm max}NS^{-}(f)|f:V(G)\rightarrow W}%$ is a bijection}. For bijections %${f:V(G)\rightarrow \{1,2,\ldots,n\}}%$ we consider the parameters NS[G], NS(G), NS−[G] and NS−(G), as well as two parameters minimizing the maximum difference in neighborhood sums. © Springer Basel AG 2011 |
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An Introduction to Closed/Open Neighborhood Sums: Minimax, Maximin, and Spread |
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https://dx.doi.org/10.1007/s11786-011-0075-4 |
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| score |
7.3992996 |