A fully benzenoid system has a unique maximum cardinality resonant set

Abstract A benzenoid system is a 2-connected plane graph such that its each inner face is a regular hexagon of side length 1. A benzenoid system is Kekuléan if it has a perfect matching. Let P be a set of hexagons of a Kekuléan benzenoid system B. The set P is called a resonant set of B if the hexag...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Gutman, Ivan [verfasserIn] Salem, Khaled [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2009

Schlagwörter:	Benzenoid system Perfect matching Resonant set Clar formula

Übergeordnetes Werk:	Enthalten in: Acta applicandae mathematicae - [S.l.] : Proquest, 1983, 112(2009), 1 vom: 06. Okt., Seite 15-19
Übergeordnetes Werk:	volume:112 ; year:2009 ; number:1 ; day:06 ; month:10 ; pages:15-19

Links:	Volltext

DOI / URN:	10.1007/s10440-009-9550-1

Katalog-ID:	SPR010081739

Internformat


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520			\|a Abstract A benzenoid system is a 2-connected plane graph such that its each inner face is a regular hexagon of side length 1. A benzenoid system is Kekuléan if it has a perfect matching. Let P be a set of hexagons of a Kekuléan benzenoid system B. The set P is called a resonant set of B if the hexagons in P are pair-wise disjoint and the subgraph B−P (obtained by deleting from B the vertices of the hexagons in P) is either empty or has a perfect matching. It was shown (Gutman in Wiss. Z. Thechn. Hochsch. Ilmenau 29:57–65, 1983; Zheng and Chen in Graphs Comb. 1:295–298, 1985) that for every maximum cardinality resonant set P of a Kekuléan benzenoid system B, the subgraph B−P is either empty or has a unique perfect matching. A Kekuléan benzenoid system B is said to be fully benzenoid if there exists a maximum cardinality resonant set P of B, such that the subgraph B−P is empty. It is shown that a fully benzenoid system has a unique maximum cardinality resonant set, a well-known statement that, so far, has remained without a rigorous proof.
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650		4	\|a Resonant set \|7 (dpeaa)DE-He213
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700	1		\|a Salem, Khaled \|e verfasserin \|4 aut
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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_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_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_206
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_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_2070
912			\|a GBV_ILN_2086
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_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_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
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Indexfelder

author_variant	i g ig k s ks
matchkey_str	article:15729036:2009----::flyeznissehsuiumxmmadn
hierarchy_sort_str	2009
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publishDate	2009
allfields	10.1007/s10440-009-9550-1 doi (DE-627)SPR010081739 (SPR)s10440-009-9550-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.80 bkl Gutman, Ivan verfasserin aut A fully benzenoid system has a unique maximum cardinality resonant set 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract A benzenoid system is a 2-connected plane graph such that its each inner face is a regular hexagon of side length 1. A benzenoid system is Kekuléan if it has a perfect matching. Let P be a set of hexagons of a Kekuléan benzenoid system B. The set P is called a resonant set of B if the hexagons in P are pair-wise disjoint and the subgraph B−P (obtained by deleting from B the vertices of the hexagons in P) is either empty or has a perfect matching. It was shown (Gutman in Wiss. Z. Thechn. Hochsch. Ilmenau 29:57–65, 1983; Zheng and Chen in Graphs Comb. 1:295–298, 1985) that for every maximum cardinality resonant set P of a Kekuléan benzenoid system B, the subgraph B−P is either empty or has a unique perfect matching. A Kekuléan benzenoid system B is said to be fully benzenoid if there exists a maximum cardinality resonant set P of B, such that the subgraph B−P is empty. It is shown that a fully benzenoid system has a unique maximum cardinality resonant set, a well-known statement that, so far, has remained without a rigorous proof. Benzenoid system (dpeaa)DE-He213 Perfect matching (dpeaa)DE-He213 Resonant set (dpeaa)DE-He213 Clar formula (dpeaa)DE-He213 Salem, Khaled verfasserin aut Enthalten in Acta applicandae mathematicae [S.l.] : Proquest, 1983 112(2009), 1 vom: 06. Okt., Seite 15-19 (DE-627)271176105 (DE-600)1479016-6 1572-9036 nnns volume:112 year:2009 number:1 day:06 month:10 pages:15-19 https://dx.doi.org/10.1007/s10440-009-9550-1 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_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_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_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 112 2009 1 06 10 15-19
spelling	10.1007/s10440-009-9550-1 doi (DE-627)SPR010081739 (SPR)s10440-009-9550-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.80 bkl Gutman, Ivan verfasserin aut A fully benzenoid system has a unique maximum cardinality resonant set 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract A benzenoid system is a 2-connected plane graph such that its each inner face is a regular hexagon of side length 1. A benzenoid system is Kekuléan if it has a perfect matching. Let P be a set of hexagons of a Kekuléan benzenoid system B. The set P is called a resonant set of B if the hexagons in P are pair-wise disjoint and the subgraph B−P (obtained by deleting from B the vertices of the hexagons in P) is either empty or has a perfect matching. It was shown (Gutman in Wiss. Z. Thechn. Hochsch. Ilmenau 29:57–65, 1983; Zheng and Chen in Graphs Comb. 1:295–298, 1985) that for every maximum cardinality resonant set P of a Kekuléan benzenoid system B, the subgraph B−P is either empty or has a unique perfect matching. A Kekuléan benzenoid system B is said to be fully benzenoid if there exists a maximum cardinality resonant set P of B, such that the subgraph B−P is empty. It is shown that a fully benzenoid system has a unique maximum cardinality resonant set, a well-known statement that, so far, has remained without a rigorous proof. Benzenoid system (dpeaa)DE-He213 Perfect matching (dpeaa)DE-He213 Resonant set (dpeaa)DE-He213 Clar formula (dpeaa)DE-He213 Salem, Khaled verfasserin aut Enthalten in Acta applicandae mathematicae [S.l.] : Proquest, 1983 112(2009), 1 vom: 06. Okt., Seite 15-19 (DE-627)271176105 (DE-600)1479016-6 1572-9036 nnns volume:112 year:2009 number:1 day:06 month:10 pages:15-19 https://dx.doi.org/10.1007/s10440-009-9550-1 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_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_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_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 112 2009 1 06 10 15-19
allfields_unstemmed	10.1007/s10440-009-9550-1 doi (DE-627)SPR010081739 (SPR)s10440-009-9550-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.80 bkl Gutman, Ivan verfasserin aut A fully benzenoid system has a unique maximum cardinality resonant set 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract A benzenoid system is a 2-connected plane graph such that its each inner face is a regular hexagon of side length 1. A benzenoid system is Kekuléan if it has a perfect matching. Let P be a set of hexagons of a Kekuléan benzenoid system B. The set P is called a resonant set of B if the hexagons in P are pair-wise disjoint and the subgraph B−P (obtained by deleting from B the vertices of the hexagons in P) is either empty or has a perfect matching. It was shown (Gutman in Wiss. Z. Thechn. Hochsch. Ilmenau 29:57–65, 1983; Zheng and Chen in Graphs Comb. 1:295–298, 1985) that for every maximum cardinality resonant set P of a Kekuléan benzenoid system B, the subgraph B−P is either empty or has a unique perfect matching. A Kekuléan benzenoid system B is said to be fully benzenoid if there exists a maximum cardinality resonant set P of B, such that the subgraph B−P is empty. It is shown that a fully benzenoid system has a unique maximum cardinality resonant set, a well-known statement that, so far, has remained without a rigorous proof. Benzenoid system (dpeaa)DE-He213 Perfect matching (dpeaa)DE-He213 Resonant set (dpeaa)DE-He213 Clar formula (dpeaa)DE-He213 Salem, Khaled verfasserin aut Enthalten in Acta applicandae mathematicae [S.l.] : Proquest, 1983 112(2009), 1 vom: 06. Okt., Seite 15-19 (DE-627)271176105 (DE-600)1479016-6 1572-9036 nnns volume:112 year:2009 number:1 day:06 month:10 pages:15-19 https://dx.doi.org/10.1007/s10440-009-9550-1 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_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_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_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 112 2009 1 06 10 15-19
allfieldsGer	10.1007/s10440-009-9550-1 doi (DE-627)SPR010081739 (SPR)s10440-009-9550-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.80 bkl Gutman, Ivan verfasserin aut A fully benzenoid system has a unique maximum cardinality resonant set 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract A benzenoid system is a 2-connected plane graph such that its each inner face is a regular hexagon of side length 1. A benzenoid system is Kekuléan if it has a perfect matching. Let P be a set of hexagons of a Kekuléan benzenoid system B. The set P is called a resonant set of B if the hexagons in P are pair-wise disjoint and the subgraph B−P (obtained by deleting from B the vertices of the hexagons in P) is either empty or has a perfect matching. It was shown (Gutman in Wiss. Z. Thechn. Hochsch. Ilmenau 29:57–65, 1983; Zheng and Chen in Graphs Comb. 1:295–298, 1985) that for every maximum cardinality resonant set P of a Kekuléan benzenoid system B, the subgraph B−P is either empty or has a unique perfect matching. A Kekuléan benzenoid system B is said to be fully benzenoid if there exists a maximum cardinality resonant set P of B, such that the subgraph B−P is empty. It is shown that a fully benzenoid system has a unique maximum cardinality resonant set, a well-known statement that, so far, has remained without a rigorous proof. Benzenoid system (dpeaa)DE-He213 Perfect matching (dpeaa)DE-He213 Resonant set (dpeaa)DE-He213 Clar formula (dpeaa)DE-He213 Salem, Khaled verfasserin aut Enthalten in Acta applicandae mathematicae [S.l.] : Proquest, 1983 112(2009), 1 vom: 06. Okt., Seite 15-19 (DE-627)271176105 (DE-600)1479016-6 1572-9036 nnns volume:112 year:2009 number:1 day:06 month:10 pages:15-19 https://dx.doi.org/10.1007/s10440-009-9550-1 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_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_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_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 112 2009 1 06 10 15-19
allfieldsSound	10.1007/s10440-009-9550-1 doi (DE-627)SPR010081739 (SPR)s10440-009-9550-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.80 bkl Gutman, Ivan verfasserin aut A fully benzenoid system has a unique maximum cardinality resonant set 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract A benzenoid system is a 2-connected plane graph such that its each inner face is a regular hexagon of side length 1. A benzenoid system is Kekuléan if it has a perfect matching. Let P be a set of hexagons of a Kekuléan benzenoid system B. The set P is called a resonant set of B if the hexagons in P are pair-wise disjoint and the subgraph B−P (obtained by deleting from B the vertices of the hexagons in P) is either empty or has a perfect matching. It was shown (Gutman in Wiss. Z. Thechn. Hochsch. Ilmenau 29:57–65, 1983; Zheng and Chen in Graphs Comb. 1:295–298, 1985) that for every maximum cardinality resonant set P of a Kekuléan benzenoid system B, the subgraph B−P is either empty or has a unique perfect matching. A Kekuléan benzenoid system B is said to be fully benzenoid if there exists a maximum cardinality resonant set P of B, such that the subgraph B−P is empty. It is shown that a fully benzenoid system has a unique maximum cardinality resonant set, a well-known statement that, so far, has remained without a rigorous proof. Benzenoid system (dpeaa)DE-He213 Perfect matching (dpeaa)DE-He213 Resonant set (dpeaa)DE-He213 Clar formula (dpeaa)DE-He213 Salem, Khaled verfasserin aut Enthalten in Acta applicandae mathematicae [S.l.] : Proquest, 1983 112(2009), 1 vom: 06. Okt., Seite 15-19 (DE-627)271176105 (DE-600)1479016-6 1572-9036 nnns volume:112 year:2009 number:1 day:06 month:10 pages:15-19 https://dx.doi.org/10.1007/s10440-009-9550-1 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_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_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_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 112 2009 1 06 10 15-19
language	English
source	Enthalten in Acta applicandae mathematicae 112(2009), 1 vom: 06. Okt., Seite 15-19 volume:112 year:2009 number:1 day:06 month:10 pages:15-19
sourceStr	Enthalten in Acta applicandae mathematicae 112(2009), 1 vom: 06. Okt., Seite 15-19 volume:112 year:2009 number:1 day:06 month:10 pages:15-19
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Benzenoid system Perfect matching Resonant set Clar formula
dewey-raw	510
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container_title	Acta applicandae mathematicae
authorswithroles_txt_mv	Gutman, Ivan @@aut@@ Salem, Khaled @@aut@@
publishDateDaySort_date	2009-10-06T00:00:00Z
hierarchy_top_id	271176105
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id	SPR010081739
language_de	englisch
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author	Gutman, Ivan
spellingShingle	Gutman, Ivan ddc 510 bkl 31.80 misc Benzenoid system misc Perfect matching misc Resonant set misc Clar formula A fully benzenoid system has a unique maximum cardinality resonant set
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topic_title	510 ASE 31.80 bkl A fully benzenoid system has a unique maximum cardinality resonant set Benzenoid system (dpeaa)DE-He213 Perfect matching (dpeaa)DE-He213 Resonant set (dpeaa)DE-He213 Clar formula (dpeaa)DE-He213
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title	A fully benzenoid system has a unique maximum cardinality resonant set
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title_full	A fully benzenoid system has a unique maximum cardinality resonant set
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title_sort	fully benzenoid system has a unique maximum cardinality resonant set
title_auth	A fully benzenoid system has a unique maximum cardinality resonant set
abstract	Abstract A benzenoid system is a 2-connected plane graph such that its each inner face is a regular hexagon of side length 1. A benzenoid system is Kekuléan if it has a perfect matching. Let P be a set of hexagons of a Kekuléan benzenoid system B. The set P is called a resonant set of B if the hexagons in P are pair-wise disjoint and the subgraph B−P (obtained by deleting from B the vertices of the hexagons in P) is either empty or has a perfect matching. It was shown (Gutman in Wiss. Z. Thechn. Hochsch. Ilmenau 29:57–65, 1983; Zheng and Chen in Graphs Comb. 1:295–298, 1985) that for every maximum cardinality resonant set P of a Kekuléan benzenoid system B, the subgraph B−P is either empty or has a unique perfect matching. A Kekuléan benzenoid system B is said to be fully benzenoid if there exists a maximum cardinality resonant set P of B, such that the subgraph B−P is empty. It is shown that a fully benzenoid system has a unique maximum cardinality resonant set, a well-known statement that, so far, has remained without a rigorous proof.
abstractGer	Abstract A benzenoid system is a 2-connected plane graph such that its each inner face is a regular hexagon of side length 1. A benzenoid system is Kekuléan if it has a perfect matching. Let P be a set of hexagons of a Kekuléan benzenoid system B. The set P is called a resonant set of B if the hexagons in P are pair-wise disjoint and the subgraph B−P (obtained by deleting from B the vertices of the hexagons in P) is either empty or has a perfect matching. It was shown (Gutman in Wiss. Z. Thechn. Hochsch. Ilmenau 29:57–65, 1983; Zheng and Chen in Graphs Comb. 1:295–298, 1985) that for every maximum cardinality resonant set P of a Kekuléan benzenoid system B, the subgraph B−P is either empty or has a unique perfect matching. A Kekuléan benzenoid system B is said to be fully benzenoid if there exists a maximum cardinality resonant set P of B, such that the subgraph B−P is empty. It is shown that a fully benzenoid system has a unique maximum cardinality resonant set, a well-known statement that, so far, has remained without a rigorous proof.
abstract_unstemmed	Abstract A benzenoid system is a 2-connected plane graph such that its each inner face is a regular hexagon of side length 1. A benzenoid system is Kekuléan if it has a perfect matching. Let P be a set of hexagons of a Kekuléan benzenoid system B. The set P is called a resonant set of B if the hexagons in P are pair-wise disjoint and the subgraph B−P (obtained by deleting from B the vertices of the hexagons in P) is either empty or has a perfect matching. It was shown (Gutman in Wiss. Z. Thechn. Hochsch. Ilmenau 29:57–65, 1983; Zheng and Chen in Graphs Comb. 1:295–298, 1985) that for every maximum cardinality resonant set P of a Kekuléan benzenoid system B, the subgraph B−P is either empty or has a unique perfect matching. A Kekuléan benzenoid system B is said to be fully benzenoid if there exists a maximum cardinality resonant set P of B, such that the subgraph B−P is empty. It is shown that a fully benzenoid system has a unique maximum cardinality resonant set, a well-known statement that, so far, has remained without a rigorous proof.
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container_issue	1
title_short	A fully benzenoid system has a unique maximum cardinality resonant set
url	https://dx.doi.org/10.1007/s10440-009-9550-1
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author2	Salem, Khaled
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doi_str	10.1007/s10440-009-9550-1
up_date	2024-07-03T13:50:22.147Z
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