Extremal Digraphs for an Upper Bound on the Double Roman Domination Number

Abstract A doubleRoman dominating function of a digraph D is a function %$f:V\longrightarrow \{0,1,2,3\}%$ such that every vertex u for which %$f(u)=0%$ has an in-neighbor v for which %$f(v)=3%$ or at least two in-neighbors assigned 2 under f, while if %$f(u)=1%$, then the vertex u must have at leas...
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Autor*in:	Ouldrabah, Lyes [verfasserIn] Blidia, Mostafa Bouchou, Ahmed Volkmann, Lutz

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	Double Roman domination Digraph Oriented Graph Tournament

Anmerkung:	© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Übergeordnetes Werk:	Enthalten in: Bulletin of the Malaysian Mathematical Sciences Society - [Singapore] : Springer Singapore, 2000, 43(2019), 2 vom: 05. Feb., Seite 1153-1162
Übergeordnetes Werk:	volume:43 ; year:2019 ; number:2 ; day:05 ; month:02 ; pages:1153-1162

Links:	Volltext

DOI / URN:	10.1007/s40840-019-00735-7

Katalog-ID:	SPR037905694

Internformat


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520			\|a Abstract A doubleRoman dominating function of a digraph D is a function %$f:V\longrightarrow \{0,1,2,3\}%$ such that every vertex u for which %$f(u)=0%$ has an in-neighbor v for which %$f(v)=3%$ or at least two in-neighbors assigned 2 under f, while if %$f(u)=1%$, then the vertex u must have at least one in-neighbor assigned 2 or 3. The weight of a double Roman dominating function is the value %$f(V)=\sum _{u\in V}f(u)%$. The minimum weight of a double Roman dominating function of a digraph D is called the double Roman domination number of D, denoted by %$\gamma _{dR}\left( D\right) %$. This paper gives a descriptive characterization for some classes of digraphs satisfying %$\gamma _{dR}(D)=2\left( n-\Delta ^{+}(D)\right) +1%$. Also, a descriptive characterization for digraphs D of order %$n\ge 4%$ for which %$\gamma _{dR}(D)+\gamma _{dR}({\overline{D}})=2n+3%$ holds where %${\overline{D}}%$ is the complement of D.
650		4	\|a Double Roman domination \|7 (dpeaa)DE-He213
650		4	\|a Digraph \|7 (dpeaa)DE-He213
650		4	\|a Oriented Graph \|7 (dpeaa)DE-He213
650		4	\|a Tournament \|7 (dpeaa)DE-He213
700	1		\|a Blidia, Mostafa \|4 aut
700	1		\|a Bouchou, Ahmed \|4 aut
700	1		\|a Volkmann, Lutz \|4 aut
773	0	8	\|i Enthalten in \|t Bulletin of the Malaysian Mathematical Sciences Society \|d [Singapore] : Springer Singapore, 2000 \|g 43(2019), 2 vom: 05. Feb., Seite 1153-1162 \|w (DE-627)843984465 \|w (DE-600)2842782-8 \|x 2180-4206 \|7 nnns
773	1	8	\|g volume:43 \|g year:2019 \|g number:2 \|g day:05 \|g month:02 \|g pages:1153-1162
856	4	0	\|u https://dx.doi.org/10.1007/s40840-019-00735-7 \|z lizenzpflichtig \|3 Volltext
912			\|a GBV_USEFLAG_A
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912			\|a GBV_ILN_20
912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
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_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_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_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_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_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
951			\|a AR
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author_variant	l o lo m b mb a b ab l v lv
matchkey_str	article:21804206:2019----::xrmlirpsoaupronoteobeo
hierarchy_sort_str	2019
publishDate	2019
allfields	10.1007/s40840-019-00735-7 doi (DE-627)SPR037905694 (SPR)s40840-019-00735-7-e DE-627 ger DE-627 rakwb eng Ouldrabah, Lyes verfasserin aut Extremal Digraphs for an Upper Bound on the Double Roman Domination Number 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019 Abstract A doubleRoman dominating function of a digraph D is a function %$f:V\longrightarrow \{0,1,2,3\}%$ such that every vertex u for which %$f(u)=0%$ has an in-neighbor v for which %$f(v)=3%$ or at least two in-neighbors assigned 2 under f, while if %$f(u)=1%$, then the vertex u must have at least one in-neighbor assigned 2 or 3. The weight of a double Roman dominating function is the value %$f(V)=\sum _{u\in V}f(u)%$. The minimum weight of a double Roman dominating function of a digraph D is called the double Roman domination number of D, denoted by %$\gamma _{dR}\left( D\right) %$. This paper gives a descriptive characterization for some classes of digraphs satisfying %$\gamma _{dR}(D)=2\left( n-\Delta ^{+}(D)\right) +1%$. Also, a descriptive characterization for digraphs D of order %$n\ge 4%$ for which %$\gamma _{dR}(D)+\gamma _{dR}({\overline{D}})=2n+3%$ holds where %${\overline{D}}%$ is the complement of D. Double Roman domination (dpeaa)DE-He213 Digraph (dpeaa)DE-He213 Oriented Graph (dpeaa)DE-He213 Tournament (dpeaa)DE-He213 Blidia, Mostafa aut Bouchou, Ahmed aut Volkmann, Lutz aut Enthalten in Bulletin of the Malaysian Mathematical Sciences Society [Singapore] : Springer Singapore, 2000 43(2019), 2 vom: 05. Feb., Seite 1153-1162 (DE-627)843984465 (DE-600)2842782-8 2180-4206 nnns volume:43 year:2019 number:2 day:05 month:02 pages:1153-1162 https://dx.doi.org/10.1007/s40840-019-00735-7 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_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_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_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_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 43 2019 2 05 02 1153-1162
spelling	10.1007/s40840-019-00735-7 doi (DE-627)SPR037905694 (SPR)s40840-019-00735-7-e DE-627 ger DE-627 rakwb eng Ouldrabah, Lyes verfasserin aut Extremal Digraphs for an Upper Bound on the Double Roman Domination Number 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019 Abstract A doubleRoman dominating function of a digraph D is a function %$f:V\longrightarrow \{0,1,2,3\}%$ such that every vertex u for which %$f(u)=0%$ has an in-neighbor v for which %$f(v)=3%$ or at least two in-neighbors assigned 2 under f, while if %$f(u)=1%$, then the vertex u must have at least one in-neighbor assigned 2 or 3. The weight of a double Roman dominating function is the value %$f(V)=\sum _{u\in V}f(u)%$. The minimum weight of a double Roman dominating function of a digraph D is called the double Roman domination number of D, denoted by %$\gamma _{dR}\left( D\right) %$. This paper gives a descriptive characterization for some classes of digraphs satisfying %$\gamma _{dR}(D)=2\left( n-\Delta ^{+}(D)\right) +1%$. Also, a descriptive characterization for digraphs D of order %$n\ge 4%$ for which %$\gamma _{dR}(D)+\gamma _{dR}({\overline{D}})=2n+3%$ holds where %${\overline{D}}%$ is the complement of D. Double Roman domination (dpeaa)DE-He213 Digraph (dpeaa)DE-He213 Oriented Graph (dpeaa)DE-He213 Tournament (dpeaa)DE-He213 Blidia, Mostafa aut Bouchou, Ahmed aut Volkmann, Lutz aut Enthalten in Bulletin of the Malaysian Mathematical Sciences Society [Singapore] : Springer Singapore, 2000 43(2019), 2 vom: 05. Feb., Seite 1153-1162 (DE-627)843984465 (DE-600)2842782-8 2180-4206 nnns volume:43 year:2019 number:2 day:05 month:02 pages:1153-1162 https://dx.doi.org/10.1007/s40840-019-00735-7 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_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_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_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_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 43 2019 2 05 02 1153-1162
allfields_unstemmed	10.1007/s40840-019-00735-7 doi (DE-627)SPR037905694 (SPR)s40840-019-00735-7-e DE-627 ger DE-627 rakwb eng Ouldrabah, Lyes verfasserin aut Extremal Digraphs for an Upper Bound on the Double Roman Domination Number 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019 Abstract A doubleRoman dominating function of a digraph D is a function %$f:V\longrightarrow \{0,1,2,3\}%$ such that every vertex u for which %$f(u)=0%$ has an in-neighbor v for which %$f(v)=3%$ or at least two in-neighbors assigned 2 under f, while if %$f(u)=1%$, then the vertex u must have at least one in-neighbor assigned 2 or 3. The weight of a double Roman dominating function is the value %$f(V)=\sum _{u\in V}f(u)%$. The minimum weight of a double Roman dominating function of a digraph D is called the double Roman domination number of D, denoted by %$\gamma _{dR}\left( D\right) %$. This paper gives a descriptive characterization for some classes of digraphs satisfying %$\gamma _{dR}(D)=2\left( n-\Delta ^{+}(D)\right) +1%$. Also, a descriptive characterization for digraphs D of order %$n\ge 4%$ for which %$\gamma _{dR}(D)+\gamma _{dR}({\overline{D}})=2n+3%$ holds where %${\overline{D}}%$ is the complement of D. Double Roman domination (dpeaa)DE-He213 Digraph (dpeaa)DE-He213 Oriented Graph (dpeaa)DE-He213 Tournament (dpeaa)DE-He213 Blidia, Mostafa aut Bouchou, Ahmed aut Volkmann, Lutz aut Enthalten in Bulletin of the Malaysian Mathematical Sciences Society [Singapore] : Springer Singapore, 2000 43(2019), 2 vom: 05. Feb., Seite 1153-1162 (DE-627)843984465 (DE-600)2842782-8 2180-4206 nnns volume:43 year:2019 number:2 day:05 month:02 pages:1153-1162 https://dx.doi.org/10.1007/s40840-019-00735-7 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_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_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_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_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 43 2019 2 05 02 1153-1162
allfieldsGer	10.1007/s40840-019-00735-7 doi (DE-627)SPR037905694 (SPR)s40840-019-00735-7-e DE-627 ger DE-627 rakwb eng Ouldrabah, Lyes verfasserin aut Extremal Digraphs for an Upper Bound on the Double Roman Domination Number 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019 Abstract A doubleRoman dominating function of a digraph D is a function %$f:V\longrightarrow \{0,1,2,3\}%$ such that every vertex u for which %$f(u)=0%$ has an in-neighbor v for which %$f(v)=3%$ or at least two in-neighbors assigned 2 under f, while if %$f(u)=1%$, then the vertex u must have at least one in-neighbor assigned 2 or 3. The weight of a double Roman dominating function is the value %$f(V)=\sum _{u\in V}f(u)%$. The minimum weight of a double Roman dominating function of a digraph D is called the double Roman domination number of D, denoted by %$\gamma _{dR}\left( D\right) %$. This paper gives a descriptive characterization for some classes of digraphs satisfying %$\gamma _{dR}(D)=2\left( n-\Delta ^{+}(D)\right) +1%$. Also, a descriptive characterization for digraphs D of order %$n\ge 4%$ for which %$\gamma _{dR}(D)+\gamma _{dR}({\overline{D}})=2n+3%$ holds where %${\overline{D}}%$ is the complement of D. Double Roman domination (dpeaa)DE-He213 Digraph (dpeaa)DE-He213 Oriented Graph (dpeaa)DE-He213 Tournament (dpeaa)DE-He213 Blidia, Mostafa aut Bouchou, Ahmed aut Volkmann, Lutz aut Enthalten in Bulletin of the Malaysian Mathematical Sciences Society [Singapore] : Springer Singapore, 2000 43(2019), 2 vom: 05. Feb., Seite 1153-1162 (DE-627)843984465 (DE-600)2842782-8 2180-4206 nnns volume:43 year:2019 number:2 day:05 month:02 pages:1153-1162 https://dx.doi.org/10.1007/s40840-019-00735-7 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_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_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_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_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 43 2019 2 05 02 1153-1162
allfieldsSound	10.1007/s40840-019-00735-7 doi (DE-627)SPR037905694 (SPR)s40840-019-00735-7-e DE-627 ger DE-627 rakwb eng Ouldrabah, Lyes verfasserin aut Extremal Digraphs for an Upper Bound on the Double Roman Domination Number 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019 Abstract A doubleRoman dominating function of a digraph D is a function %$f:V\longrightarrow \{0,1,2,3\}%$ such that every vertex u for which %$f(u)=0%$ has an in-neighbor v for which %$f(v)=3%$ or at least two in-neighbors assigned 2 under f, while if %$f(u)=1%$, then the vertex u must have at least one in-neighbor assigned 2 or 3. The weight of a double Roman dominating function is the value %$f(V)=\sum _{u\in V}f(u)%$. The minimum weight of a double Roman dominating function of a digraph D is called the double Roman domination number of D, denoted by %$\gamma _{dR}\left( D\right) %$. This paper gives a descriptive characterization for some classes of digraphs satisfying %$\gamma _{dR}(D)=2\left( n-\Delta ^{+}(D)\right) +1%$. Also, a descriptive characterization for digraphs D of order %$n\ge 4%$ for which %$\gamma _{dR}(D)+\gamma _{dR}({\overline{D}})=2n+3%$ holds where %${\overline{D}}%$ is the complement of D. Double Roman domination (dpeaa)DE-He213 Digraph (dpeaa)DE-He213 Oriented Graph (dpeaa)DE-He213 Tournament (dpeaa)DE-He213 Blidia, Mostafa aut Bouchou, Ahmed aut Volkmann, Lutz aut Enthalten in Bulletin of the Malaysian Mathematical Sciences Society [Singapore] : Springer Singapore, 2000 43(2019), 2 vom: 05. Feb., Seite 1153-1162 (DE-627)843984465 (DE-600)2842782-8 2180-4206 nnns volume:43 year:2019 number:2 day:05 month:02 pages:1153-1162 https://dx.doi.org/10.1007/s40840-019-00735-7 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_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_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_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_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 43 2019 2 05 02 1153-1162
language	English
source	Enthalten in Bulletin of the Malaysian Mathematical Sciences Society 43(2019), 2 vom: 05. Feb., Seite 1153-1162 volume:43 year:2019 number:2 day:05 month:02 pages:1153-1162
sourceStr	Enthalten in Bulletin of the Malaysian Mathematical Sciences Society 43(2019), 2 vom: 05. Feb., Seite 1153-1162 volume:43 year:2019 number:2 day:05 month:02 pages:1153-1162
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Double Roman domination Digraph Oriented Graph Tournament
isfreeaccess_bool	false
container_title	Bulletin of the Malaysian Mathematical Sciences Society
authorswithroles_txt_mv	Ouldrabah, Lyes @@aut@@ Blidia, Mostafa @@aut@@ Bouchou, Ahmed @@aut@@ Volkmann, Lutz @@aut@@
publishDateDaySort_date	2019-02-05T00:00:00Z
hierarchy_top_id	843984465
id	SPR037905694
language_de	englisch
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR037905694</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230328211049.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201007s2019 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s40840-019-00735-7</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR037905694</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s40840-019-00735-7-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ouldrabah, Lyes</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Extremal Digraphs for an Upper Bound on the Double Roman Domination Number</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2019</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract A doubleRoman dominating function of a digraph D is a function %$f:V\longrightarrow \{0,1,2,3\}%$ such that every vertex u for which %$f(u)=0%$ has an in-neighbor v for which %$f(v)=3%$ or at least two in-neighbors assigned 2 under f, while if %$f(u)=1%$, then the vertex u must have at least one in-neighbor assigned 2 or 3. The weight of a double Roman dominating function is the value %$f(V)=\sum _{u\in V}f(u)%$. The minimum weight of a double Roman dominating function of a digraph D is called the double Roman domination number of D, denoted by %$\gamma _{dR}\left( D\right) %$. This paper gives a descriptive characterization for some classes of digraphs satisfying %$\gamma _{dR}(D)=2\left( n-\Delta ^{+}(D)\right) +1%$. Also, a descriptive characterization for digraphs D of order %$n\ge 4%$ for which %$\gamma _{dR}(D)+\gamma _{dR}({\overline{D}})=2n+3%$ holds where %${\overline{D}}%$ is the complement of D.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Double Roman domination</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Digraph</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Oriented Graph</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Tournament</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Blidia, Mostafa</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Bouchou, Ahmed</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Volkmann, Lutz</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Bulletin of the Malaysian Mathematical Sciences Society</subfield><subfield code="d">[Singapore] : Springer Singapore, 2000</subfield><subfield code="g">43(2019), 2 vom: 05. 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author	Ouldrabah, Lyes
spellingShingle	Ouldrabah, Lyes misc Double Roman domination misc Digraph misc Oriented Graph misc Tournament Extremal Digraphs for an Upper Bound on the Double Roman Domination Number
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topic_title	Extremal Digraphs for an Upper Bound on the Double Roman Domination Number Double Roman domination (dpeaa)DE-He213 Digraph (dpeaa)DE-He213 Oriented Graph (dpeaa)DE-He213 Tournament (dpeaa)DE-He213
topic	misc Double Roman domination misc Digraph misc Oriented Graph misc Tournament
topic_unstemmed	misc Double Roman domination misc Digraph misc Oriented Graph misc Tournament
topic_browse	misc Double Roman domination misc Digraph misc Oriented Graph misc Tournament
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title	Extremal Digraphs for an Upper Bound on the Double Roman Domination Number
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title_full	Extremal Digraphs for an Upper Bound on the Double Roman Domination Number
author_sort	Ouldrabah, Lyes
journal	Bulletin of the Malaysian Mathematical Sciences Society
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author_browse	Ouldrabah, Lyes Blidia, Mostafa Bouchou, Ahmed Volkmann, Lutz
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format_se	Elektronische Aufsätze
author-letter	Ouldrabah, Lyes
doi_str_mv	10.1007/s40840-019-00735-7
title_sort	extremal digraphs for an upper bound on the double roman domination number
title_auth	Extremal Digraphs for an Upper Bound on the Double Roman Domination Number
abstract	Abstract A doubleRoman dominating function of a digraph D is a function %$f:V\longrightarrow \{0,1,2,3\}%$ such that every vertex u for which %$f(u)=0%$ has an in-neighbor v for which %$f(v)=3%$ or at least two in-neighbors assigned 2 under f, while if %$f(u)=1%$, then the vertex u must have at least one in-neighbor assigned 2 or 3. The weight of a double Roman dominating function is the value %$f(V)=\sum _{u\in V}f(u)%$. The minimum weight of a double Roman dominating function of a digraph D is called the double Roman domination number of D, denoted by %$\gamma _{dR}\left( D\right) %$. This paper gives a descriptive characterization for some classes of digraphs satisfying %$\gamma _{dR}(D)=2\left( n-\Delta ^{+}(D)\right) +1%$. Also, a descriptive characterization for digraphs D of order %$n\ge 4%$ for which %$\gamma _{dR}(D)+\gamma _{dR}({\overline{D}})=2n+3%$ holds where %${\overline{D}}%$ is the complement of D. © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019
abstractGer	Abstract A doubleRoman dominating function of a digraph D is a function %$f:V\longrightarrow \{0,1,2,3\}%$ such that every vertex u for which %$f(u)=0%$ has an in-neighbor v for which %$f(v)=3%$ or at least two in-neighbors assigned 2 under f, while if %$f(u)=1%$, then the vertex u must have at least one in-neighbor assigned 2 or 3. The weight of a double Roman dominating function is the value %$f(V)=\sum _{u\in V}f(u)%$. The minimum weight of a double Roman dominating function of a digraph D is called the double Roman domination number of D, denoted by %$\gamma _{dR}\left( D\right) %$. This paper gives a descriptive characterization for some classes of digraphs satisfying %$\gamma _{dR}(D)=2\left( n-\Delta ^{+}(D)\right) +1%$. Also, a descriptive characterization for digraphs D of order %$n\ge 4%$ for which %$\gamma _{dR}(D)+\gamma _{dR}({\overline{D}})=2n+3%$ holds where %${\overline{D}}%$ is the complement of D. © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019
abstract_unstemmed	Abstract A doubleRoman dominating function of a digraph D is a function %$f:V\longrightarrow \{0,1,2,3\}%$ such that every vertex u for which %$f(u)=0%$ has an in-neighbor v for which %$f(v)=3%$ or at least two in-neighbors assigned 2 under f, while if %$f(u)=1%$, then the vertex u must have at least one in-neighbor assigned 2 or 3. The weight of a double Roman dominating function is the value %$f(V)=\sum _{u\in V}f(u)%$. The minimum weight of a double Roman dominating function of a digraph D is called the double Roman domination number of D, denoted by %$\gamma _{dR}\left( D\right) %$. This paper gives a descriptive characterization for some classes of digraphs satisfying %$\gamma _{dR}(D)=2\left( n-\Delta ^{+}(D)\right) +1%$. Also, a descriptive characterization for digraphs D of order %$n\ge 4%$ for which %$\gamma _{dR}(D)+\gamma _{dR}({\overline{D}})=2n+3%$ holds where %${\overline{D}}%$ is the complement of D. © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019
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container_issue	2
title_short	Extremal Digraphs for an Upper Bound on the Double Roman Domination Number
url	https://dx.doi.org/10.1007/s40840-019-00735-7
remote_bool	true
author2	Blidia, Mostafa Bouchou, Ahmed Volkmann, Lutz
author2Str	Blidia, Mostafa Bouchou, Ahmed Volkmann, Lutz
ppnlink	843984465
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hochschulschrift_bool	false
doi_str	10.1007/s40840-019-00735-7
up_date	2024-07-03T15:03:51.472Z
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score	7.400717

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Extremal Digraphs for an Upper Bound on the Double Roman Domination Number

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