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Geometry of Chemical Graphs: Polycycles and Two-faced Maps [Kietas viršelis]

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(Ecole Normale Supérieure, Paris),
  • Formatas: Hardback, 316 pages, aukštis x plotis x storis: 241x165x24 mm, weight: 610 g, 15 Tables, unspecified; 20 Halftones, unspecified; 275 Line drawings, unspecified; 3 Line drawings, color
  • Serija: Encyclopedia of Mathematics and its Applications
  • Išleidimo metai: 26-Jun-2008
  • Leidėjas: Cambridge University Press
  • ISBN-10: 052187307X
  • ISBN-13: 9780521873079
Kitos knygos pagal šią temą:
Geometry of Chemical Graphs: Polycycles and Two-faced MapsDidesnis paveikslėlis
  • Formatas: Hardback, 316 pages, aukštis x plotis x storis: 241x165x24 mm, weight: 610 g, 15 Tables, unspecified; 20 Halftones, unspecified; 275 Line drawings, unspecified; 3 Line drawings, color
  • Serija: Encyclopedia of Mathematics and its Applications
  • Išleidimo metai: 26-Jun-2008
  • Leidėjas: Cambridge University Press
  • ISBN-10: 052187307X
  • ISBN-13: 9780521873079
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780521873079.html
Raktažodžiai:
Mathematical tools for the study of generalisations of graphs appearing in the modelling of molecular structures.

Polycycles and symmetric polyhedra appear as generalizations of graphs in the modeling of molecular structures, such as the Nobel prize winning fullerenes, occurring in chemistry and crystallography. The chemistry has inspired and informed many interesting questions in mathematics and computer science, which in turn have suggested directions for synthesis of molecules. Here the authors give access to new results in the theory of polycycles and two-faced maps together with the relevant background material and mathematical tools for their study. Organized so that, after reading the introductory chapter, each chapter can be read independently from the others, the book should be accessible to researchers and students in graph theory, discrete geometry, and combinatorics, as well as to those in more applied areas such as mathematical chemistry and crystallography. Many of the results in the subject require the use of computer enumeration; the corresponding programs are available from the author's website.

Recenzijos

' a rich source of chemical graphs (and beyond) and their properties. It should thus serve as a standard reference for researchers in the area.' Mathematical Reviews

Daugiau informacijos

Mathematical tools for the study of generalisations of graphs appearing in the modelling of molecular structures.
Preface ix
1 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
18
1.6 Operations on maps
21
2 Two-faced maps
24
2.1 The Goldberg–Coxeter construction
28
2.2 Description of the classes
31
2.3 Computer generation of the classes
36
3 Fullerenes as tilings of surfaces
38
3.1 Classification of finite fullerenes
38
3.2 Toroidal and Klein bottle fullerenes
39
3.3 Projective fullerenes
41
3.4 Plane 3-fullerenes
42
4 Polycycles
43
4.1 (r, q)-polycycles
43
4.2 Examples
45
4.3 Cell-homomorphism and structure of (r, q)-polycycles
48
4.4 Angles and curvature
51
4.5 Polycycles on surfaces
53
5 Polycycles with given boundary
56
5.1 The problem of uniqueness of (r, q)-fillings
56
5.2 (r, 3)-filling algorithms
61
6 Symmetries of polycycles
64
6.1 Automorphism group of (r, q)-polycycles
64
6.2 Isohedral and isogonal (r, q)-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 (R, q)gen-polycycles
76
7.3 Kernel-elementary polycycles
79
7.4 Classification of elementary ({2, 3, 4, 5},)gen-polycycles
83
7.5 Classification of elementary ({2, 3}, 4)gen-polycycles
89
7.6 Classification of elementary ({2, 3}, 5)gen-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, q)-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}, k)-spheres
136
9.3 Strictly face-regular ({a, b}, k)-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)
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, b}, 3)-maps
184
11.2 Remaining questions
186
12 Spheres and tori that are aRi 187
12.1 Maps aR0
187
12.2 Maps 4R1
189
12.3 Maps 4R2
195
12.4 Maps 5R2
203
12.5 Maps 5R3
204
13 Frank-Kasper spheres and tori 218
13.1 Euler formula for ({a, b}, 3)-maps bR0
218
13.2 The major skeleton, elementary polycycles, and classification results
219
14 Spheres and tori that are bR1 225
14.1 Euler formula for ({a, b}, 3)-maps bR1
225
14.2 Elementary polycycles
229
15 Spheres and tori that are bR2 234
15.1 ({a, b}, 3)-maps bR2
234
15.2 ({5, b}, 3)-tori bR2
237
15.3 ({a, b}, 3)-spheres with a cycle of b-gons
239
16 Spheres and tori that are bR3 246
16.1 Classification of ({4, b}, 3)-maps bR3
246
16.2 ({5, b}, 3)-maps bR3
252
17 Spheres and tori that are bR4 256
17.1 ({4, b}, 3)-maps bR4
256
17.2 ({5, b}, 3)-maps bR4.
270
18 Spheres and tori that are bRj for j> or = to 5 274
18.1 Maps bR5
274
18.2 Maps bR6
281
19 Icosahedral fulleroids 284
19.1 Construction of I-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
Michel Deza is Director of Research at CNRS, Director of the Laboratoire interdisciplinaire de géométrie appliquée, and a Professor at Ecole Normale Supérieure, Paris. He is Editor-in-chief of the European Journal of Combinatorics and this is his 12th book. Mathieu Dutour Sikiri is a Researcher of Mathematics at Institut Rudjer Bokovi, Zagreb. His research interests include enumeration and extremal problems, in relation to plane graph and discrete structures; polyhedral enumeration, Lattices, Delaunay polytopes and dual description problems.