Geometry of chemical graphs: polycycles and two-faced maps
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2008
|
| Series: | Encyclopedia of mathematics and its applications
119 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 306 S. Ill., graph. Darst. |
| ISBN: | 9780521873079 |
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Record in the Search Index
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| adam_text | GEOMETRY OF CHEMICAL GRAPHS: POLY CYCLES AND TWO-FACED MAPS MICHEL DEZA
ECOLE NORMALE SUPERIEURE, PARIS, MATHIEU DUTOUR SIKIRIC RUDJER BOSKOVIC
INSTITUTE, ZAGREB CAMBRIDGE 7 UNIVERSITY CONTENTS PREFACE , PAGE, IX
INTRODUCTION 1 1.1 GRAPHS * **.* 1 1.2 TOPOLOGICAL NOTIONS 2 1.3
REPRESENTATION OF MAPS 9 1.4 SYMMETRY GROUPS OF MAPS 12 1.5 TYPES OF
REGULARITY OF MAPS . 1 8 1.6 OPERATIONS ON MAPS , 21 TWO-FACED MAPS 24
2.1 THE GOLDBERG-GOXETER CONSTRUCTION 28 2.2 DESCRIPTION OF THE CLASSES
31 2.3 COMPUTER GENERATION OF THE CLASSES , 36 FULLERENES AS TILINGS OF
SURFACES 38 3.1 CLASSIFICATION OF FINITE FULLERENES ;* . ; ,I 38 3.2
TOROIDAL AND KLEIN BOTTLE FULLERENES , , : . ;. 39 3.3 PROJECTIVE
FULLERENES * : * ; 41 3.4 PLANE 3-FULLERENES 0 ;I 42 POLYCYCLES . * .
; 43 4.1 (R, G)-POLYCYCLES , . . ; . : 43 4.2 EXAMPLES . ;I .* . * 45
4.3 CELL-HOMOMORPHISM AND STRUCTURE OF (R, ^)-POLYCYCLES 48 4.4 ANGLES
AND CURVATURE L 51 4.5 POLYCYCLES ON SURFACES 53 POLYCYCLES WITH GIVEN
BOUNDARY , * . 56 5.1 THE PROBLEM OF UNIQUENESS OF (R, ^)-FILLINGS
,*-.** * . 56 5.2 (R, 3)-FILLING ALGORITHMS A 61 VI CONTENTS 6
SYMMETRIES OF POLYCYCLES . . . 64 6.1 AUTOMORPHISM GROUP OF (R,
G)-POLYCYCLES 64 6.2 ISOHEDRAL AND ISOGONAL (R, G)-POLYCYCLES ., 65
6.3 ISOHEDRAL AND ISOGONAL (R, Q) GEN -POLYCYCLES 71 7 ELEMENTARY
POLYCYCLES 73 7.1 DECOMPOSITION OF POLYCYCLES 73 7.2 PARABOLIC AND
HYPERBOLIC ELEMENTARY (/?, Q) GEN -POLYCYCLES 76 7.3 KERNEL-ELEMENTARY
POLYCYCLES 79 7.4 CLASSIFICATION OF ELEMENTARY ({2, 3,4, 5}, 3) GEN
-POLYCYCLES 83 7.5 CLASSIFICATION OF ELEMENTARY ({2, 3}, 4) GEN
-POLYCYCLES 89 7.6 CLASSIFICATION OF ELEMENTARY ({2, 3}, 5) GOT
-POLYCYCLES 90 7.7 APPENDIX 1: 204 SPORADIC ELEMENTARY ({2, 3, 4, 5},
3)-POLYCYCLES 93 7.8 APPENDIX 2: 57 SPORADIC ELEMENTARY ({2, 3},
5)-POLYCYCLES 102 8 APPLICATIONS OF ELEMENTARY DECOMPOSITIONS TO (R,
^)-POLYCYCLES 107 8.1 EXTREMAL POLYCYCLES 108 8.2 NON-EXTENSIBLE
POLYCYCLES 116 8.3 2-EMBEDDABLE POLYCYCLES , .121 9 STRICTLY
FACE-REGULAR SPHERES AND TORI 125 9.1 STRICTLY FACE-REGULAR SPHERES 126
9.2 NON-POLYHEDRAL STRICTLY FACE-REGULAR ([A, B], &)-SPHERES , 136 9.3
STRICTLY FACE-REGULAR ({A, 6],FC)-PLANES 143 10 PARABOLIC WEAKLY
FACE-REGULAR SPHERES 168 10.1 FACE-REGULAR ({2, 6}, 3)-SPHERES 168 10.2
FACE-REGULAR ({3, 6}, 3)-SPHERES * 169 10.3 FACE-REGULAR ({4, 6},
3)-SPHERES 169 10.4 FACE-REGULAR ({5, 6}, 3)-SPHERES (FULLERENES) R 170
10.5 FACE-REGULAR ({3,4}, 4)-SPHERES 177 10.6 FACE-REGULAR ({2,3},
6)-SPHERES . ; 179 11 GENERAL PROPERTIES OF 3-VALENT FACE-REGULAR MAPS
. 181 11.1 GENERAL ({A, FC},3)-MAPS 184 11.2 REMAINING QUESTIONS 186
12 SPHERES AND TORI THAT AREAI?, 187 12.1 MAPSARO . . * , 187 12.2 MAPS
4R : 189 12.3 MAPS 4FL 2 * * 195 12.4 MAPS5R 2 ; * * * 203
12.5 MAPS57? 3 *** ** 204 CONTENTS VII 13 FRANK-KASPER SPHERES AND TORI
218 13.1 EULER FORMULA FOR ({A, B], 3)-MAPS BR 0 218 13.2 THE MAJOR
SKELETON, ELEMENTARY POLYCYCLES, AND CLASSIFICATION RESULTS 219 14
SPHERES AND TORI THAT ARE BRI 225 14.1 EULER FORMULA FOR ({A, B],
3)-MZPS BR 225 14.2 ELEMENTARY POLYCYCLES 229 15 SPHERES AND TORI THAT
ARE BRI 234 15.1 ({A, B], 3)-MAPS BR 2 234 15.2 ({5,B},3)-TORIBR 2 237
15.3 ({A, B], 3)-SPHERES WITH A CYCLE OF B-GONS 239 16 SPHERES AND TORI
THAT ARE BRJ 246 16.1 CLASSIFICATION OF ({4, B], 3)-MAPS BR 3 246 16.2
({5,B},3)-MAPSBR 3 252 17 SPHERES AND TORI THAT ARE BR 4 256 17.1 ({4,
B], 3)-MAPS BR 4 256 17.2 ({5,B},3)-MAPSBR 4 270 18 SPHERES AND TORI
THAT ARE BRJ FOR J 5 274 18.1 MAPS/? 5 274 18.2 MAPS6TF 6 281 19
ICOSAHEDRAL FULLEROIDS 284 19.1 CONSTRUCTION OF/-FULLEROIDS AND INFINITE
SERIES 285 19.2 RESTRICTIONS ON THE P-VECTORS 288 19.3 FROM THE P-
VECTORS TO THE STRUCTURES . 291 REFERENCES 295 INDEX 304
|
| adam_txt |
GEOMETRY OF CHEMICAL GRAPHS: POLY CYCLES AND TWO-FACED MAPS MICHEL DEZA
ECOLE NORMALE SUPERIEURE, PARIS, MATHIEU DUTOUR SIKIRIC RUDJER BOSKOVIC
INSTITUTE, ZAGREB CAMBRIDGE' 7 UNIVERSITY CONTENTS PREFACE , " PAGE, IX
INTRODUCTION 1 1.1 GRAPHS * **.* 1 1.2 TOPOLOGICAL NOTIONS ' 2 1.3
REPRESENTATION OF MAPS 9 1.4 SYMMETRY GROUPS OF MAPS 12 1.5 TYPES OF
REGULARITY OF MAPS . 1 8 1.6 OPERATIONS ON MAPS , 21 TWO-FACED MAPS 24
2.1 THE GOLDBERG-GOXETER CONSTRUCTION 28 2.2 DESCRIPTION OF THE CLASSES
31 2.3 COMPUTER GENERATION OF THE CLASSES , 36 FULLERENES AS TILINGS OF
SURFACES 38 3.1 CLASSIFICATION OF FINITE FULLERENES ;* . ; ,I 38 3.2
TOROIDAL AND KLEIN BOTTLE FULLERENES , , : . ;. 39 3.3 PROJECTIVE
FULLERENES * : ' * ; 41 3.4 PLANE 3-FULLERENES 0 ;I 42 POLYCYCLES . * .
; 43 4.1 (R, G)-POLYCYCLES , . . ; . : 43 4.2 EXAMPLES . ;I .* . * 45
4.3 CELL-HOMOMORPHISM AND STRUCTURE OF (R, ^)-POLYCYCLES 48 4.4 ANGLES
AND CURVATURE L ' 51 4.5 POLYCYCLES ON SURFACES 53 POLYCYCLES WITH GIVEN
BOUNDARY ' , * . 56 5.1 THE PROBLEM OF UNIQUENESS OF (R, ^)-FILLINGS
,*-.** * . 56 5.2 (R, 3)-FILLING ALGORITHMS A ' 61 VI CONTENTS 6
SYMMETRIES OF POLYCYCLES . . . 64 6.1 AUTOMORPHISM GROUP OF (R,
G)-POLYCYCLES " ' 64 6.2 ISOHEDRAL AND ISOGONAL (R, G)-POLYCYCLES ., 65
6.3 ISOHEDRAL AND ISOGONAL (R, Q) GEN -POLYCYCLES 71 7 ELEMENTARY
POLYCYCLES 73 7.1 DECOMPOSITION OF POLYCYCLES 73 7.2 PARABOLIC AND
HYPERBOLIC ELEMENTARY (/?, Q) GEN -POLYCYCLES 76 7.3 KERNEL-ELEMENTARY
POLYCYCLES 79 7.4 CLASSIFICATION OF ELEMENTARY ({2, 3,4, 5}, 3) GEN
-POLYCYCLES 83 7.5 CLASSIFICATION OF ELEMENTARY ({2, 3}, 4) GEN
-POLYCYCLES 89 7.6 CLASSIFICATION OF ELEMENTARY ({2, 3}, 5) GOT
-POLYCYCLES 90 7.7 APPENDIX 1: 204 SPORADIC ELEMENTARY ({2, 3, 4, 5},
3)-POLYCYCLES 93 7.8 APPENDIX 2: 57 SPORADIC ELEMENTARY ({2, 3},
5)-POLYCYCLES 102 8 APPLICATIONS OF ELEMENTARY DECOMPOSITIONS TO (R,
^)-POLYCYCLES 107 8.1 EXTREMAL POLYCYCLES 108 8.2 NON-EXTENSIBLE
POLYCYCLES 116 8.3 2-EMBEDDABLE POLYCYCLES , .121 9 STRICTLY
FACE-REGULAR SPHERES AND TORI 125 9.1 STRICTLY FACE-REGULAR SPHERES 126
9.2 NON-POLYHEDRAL STRICTLY FACE-REGULAR ([A, B], &)-SPHERES , 136 9.3
STRICTLY FACE-REGULAR ({A, 6],FC)-PLANES 143 10 PARABOLIC WEAKLY
FACE-REGULAR SPHERES 168 10.1 FACE-REGULAR ({2, 6}, 3)-SPHERES 168 10.2
FACE-REGULAR ({3, 6}, 3)-SPHERES * 169 10.3 FACE-REGULAR ({4, 6},
3)-SPHERES 169 10.4 FACE-REGULAR ({5, 6}, 3)-SPHERES (FULLERENES) R 170
10.5 FACE-REGULAR ({3,4}, 4)-SPHERES 177 10.6 FACE-REGULAR ({2,3},
6)-SPHERES . ; 179 11 GENERAL PROPERTIES OF 3-VALENT FACE-REGULAR MAPS
'". 181 11.1 GENERAL ({A, FC},3)-MAPS 184 11.2 REMAINING QUESTIONS 186
12 SPHERES AND TORI THAT AREAI?, 187 12.1 MAPSARO '.'.'*', 187 12.2 MAPS
4R : ' ' ''' 189 12.3 MAPS 4FL 2 * ' * 195 12.4 MAPS5R 2 ; * * *' 203
12.5 MAPS57? 3 *** ** 204 CONTENTS VII 13 FRANK-KASPER SPHERES AND TORI
218 13.1 EULER FORMULA FOR ({A, B], 3)-MAPS BR 0 218 13.2 THE MAJOR
SKELETON, ELEMENTARY POLYCYCLES, AND CLASSIFICATION RESULTS 219 14
SPHERES AND TORI THAT ARE BRI 225 14.1 EULER FORMULA FOR ({A, B],
3)-MZPS BR\ 225 14.2 ELEMENTARY POLYCYCLES 229 15 SPHERES AND TORI THAT
ARE BRI 234 15.1 ({A, B], 3)-MAPS BR 2 234 15.2 ({5,B},3)-TORIBR 2 237
15.3 ({A, B], 3)-SPHERES WITH A CYCLE OF B-GONS 239 16 SPHERES AND TORI
THAT ARE BRJ 246 16.1 CLASSIFICATION OF ({4, B], 3)-MAPS BR 3 246 16.2
({5,B},3)-MAPSBR 3 252 17 SPHERES AND TORI THAT ARE BR 4 256 17.1 ({4,
B], 3)-MAPS BR 4 256 17.2 ({5,B},3)-MAPSBR 4 270 18 SPHERES AND TORI
THAT ARE BRJ FOR J 5 274 18.1 MAPS/? 5 274 18.2 MAPS6TF 6 281 19
ICOSAHEDRAL FULLEROIDS 284 19.1 CONSTRUCTION OF/-FULLEROIDS AND INFINITE
SERIES 285 19.2 RESTRICTIONS ON THE P-VECTORS 288 19.3 FROM THE P-
VECTORS TO THE STRUCTURES . 291 REFERENCES 295 INDEX 304 |
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| series2 | Encyclopedia of mathematics and its applications |
| spelling | Deza, Michel 1939- Verfasser (DE-588)118064495 aut Geometry of chemical graphs polycycles and two-faced maps Michel Deza ; Mathieu Dutour Sikirić Cambridge Cambridge Univ. Press 2008 X, 306 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 119 Chemical models - Mathematics Graphentheoretisches Modell Molecules - Models Molekül Chemie - Geometrie idsbb Geometrie - Chemie idsbb Mathematik Chemical models Mathematics Molecules Models Dutour Sikirić, Mathieu Verfasser aut Encyclopedia of mathematics and its applications 119 (DE-604)BV000903719 119 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016993046&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Deza, Michel 1939- Dutour Sikirić, Mathieu Geometry of chemical graphs polycycles and two-faced maps Encyclopedia of mathematics and its applications Chemical models - Mathematics Graphentheoretisches Modell Molecules - Models Molekül Chemie - Geometrie idsbb Geometrie - Chemie idsbb Mathematik Chemical models Mathematics Molecules Models |
| title | Geometry of chemical graphs polycycles and two-faced maps |
| title_auth | Geometry of chemical graphs polycycles and two-faced maps |
| title_exact_search | Geometry of chemical graphs polycycles and two-faced maps |
| title_exact_search_txtP | Geometry of chemical graphs polycycles and two-faced maps |
| title_full | Geometry of chemical graphs polycycles and two-faced maps Michel Deza ; Mathieu Dutour Sikirić |
| title_fullStr | Geometry of chemical graphs polycycles and two-faced maps Michel Deza ; Mathieu Dutour Sikirić |
| title_full_unstemmed | Geometry of chemical graphs polycycles and two-faced maps Michel Deza ; Mathieu Dutour Sikirić |
| title_short | Geometry of chemical graphs |
| title_sort | geometry of chemical graphs polycycles and two faced maps |
| title_sub | polycycles and two-faced maps |
| topic | Chemical models - Mathematics Graphentheoretisches Modell Molecules - Models Molekül Chemie - Geometrie idsbb Geometrie - Chemie idsbb Mathematik Chemical models Mathematics Molecules Models |
| topic_facet | Chemical models - Mathematics Graphentheoretisches Modell Molecules - Models Molekül Chemie - Geometrie Geometrie - Chemie Mathematik Chemical models Mathematics Molecules Models |
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