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The Resource Geometric Structure of Chemistry-Relevant Graphs : Zigzags and Central Circuits

Geometric Structure of Chemistry-Relevant Graphs : Zigzags and Central Circuits

Label
Geometric Structure of Chemistry-Relevant Graphs : Zigzags and Central Circuits
Title
Geometric Structure of Chemistry-Relevant Graphs
Title remainder
Zigzags and Central Circuits
Creator
Contributor
Subject
Language
eng
Summary
The central theme of the present book is zigzags and central-circuits of three- or four-regular plane graphs, which allow a double covering or covering of the edgeset to be obtained. The book presents zigzag and central circuit structures of geometric fullerenes and several other classes of graph of interest in the fields of chemistry and mathematics. It also discusses the symmetries, parameterization and the Goldberg-Coxeter construction for those graphs. It is the first book on this subject, presenting full structure theory of such graphs. While many previous publications only addressed particular questions about selected graphs, this book is based on numerous computations and presents extensive data (tables and figures), as well as algorithmic and computational information. It will be of interest to researchers and students of discrete geometry, mathematical chemistry and combinatorics, as well as to lay mathematicians
Member of
Cataloging source
MiAaPQ
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Forum for Interdisciplinary Mathematics
Series volume
v.1
Geometric Structure of Chemistry-Relevant Graphs : Zigzags and Central Circuits
Label
Geometric Structure of Chemistry-Relevant Graphs : Zigzags and Central Circuits
Link
http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/rpi/detail.action?docID=2096177
Publication
Copyright
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Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Preface -- Contents -- About the Authors -- 1 Introduction: Main ZC-Notions -- 1.1 Graphs -- 1.2 Symmetries -- 1.3 Zigzag and Central Circuits -- 1.4 Curvature of Faces -- 1.5 Bifaced Maps -- 1.6 Computer Generation of the Families -- References -- 2 Zigzags of Fullerenes and c-Disk-Fullerenes -- 2.1 Zigzags Statistics for Small Fullerenes -- 2.2 Kekulé Graphs -- 2.3 z-knot Fullerenes -- 2.4 Railroads in Fullerenes -- 2.5 Fullerenes 5v with Simple Zigzags -- 2.6 Tight Fullerenes -- 2.7 Disk-Fullerenes -- References -- 3 Zigzags and Railroads of Spheres 3v and 4v -- 3.1 General Results for Plane Graphs -- 3.2 Graphs 3v -- 3.3 Graphs 4v -- 3.4 Railroads and Pseudo-Roads -- References -- 4 ZC-Circuits of 4-Regular and Self-dual {2, 3, 4}-Spheres -- 4.1 Central Circuits of i-hedrites -- 4.2 Connectivity and Symmetries of i-hedrites -- 4.3 Tight i-hedrites and All Pure Tight i-hedrites -- 4.4 Enumeration and Generation of i-hedrites -- 4.4.1 8-hedrites -- 4.4.2 4-hedrites -- 4.4.3 5-hedrites -- 4.4.4 6-hedrites -- 4.4.5 7-hedrites -- 4.4.6 Generation of i-hedrites -- 4.5 Self-dual {1, 2, 3, 4}-Spheres -- References -- 5 ZC-Circuits of 5- and 6-Regular Spheres -- 5.1 Icosahedrites -- 5.2 Generation Method of ({1,2,3},6)-Spheres -- 5.3 Symmetry Groups of the ({1,2,3},6)-Spheres -- 5.4 The Goldberg--Coxeter Construction for 6-Regular Graphs -- 5.5 Zigzags and Central Circuits of 6-Regular Graphs -- References -- 6 Goldberg--Coxeter Construction and Parametrization -- 6.1 The Complex Number Rings mathbbZ[}] and mathbbZ[i] -- 6.2 The GC-Construction for 3- and 4-Regular Graphs -- 6.3 Classes of Graphs -- 6.4 Triangulations of Oriented Maps -- 6.5 Two Parameters Constructions -- 6.6 General Case of Parameterization of Maps on Oriented Surfaces -- 6.7 Thurston's Theory for Maps of Positive Curvature
  • 6.8 Extensions and Other Cases of Parameter Descriptions -- References -- 7 ZC-Circuits of Goldberg--Coxeter Construction -- 7.1 Directed Edge Formalism -- 7.2 ZC-Circuits of Inflation Graphs -- 7.3 The Moving Group and the (k,l)-product -- 7.4 The Stabilizer Group -- 7.5 The GC-Construction on Basic Plane Graphs -- 7.6 Projections of ZC-Transitive GCk,l(G0) for Some Graphs G0 -- 7.7 Zigzags of Other Parameter Constructions -- References -- 8 Zigzags of Polytopes and Complexes -- 8.1 Zigzags for d-Dimensional Complexes -- 8.2 Z-Structure of Some Generalizations of Regular d-Polytopes -- 8.3 Wythoff Kaleidoscope Construction -- 8.4 Wilson--Lins Triality -- References -- Index
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Dimensions
unknown
http://library.link/vocab/discovery_link
{'f': 'http://opac.lib.rpi.edu/record=b3747022'}
Extent
1 online resource (220 pages)
Form of item
online
Isbn
9788132224495
Media category
computer
Media MARC source
rdamedia
Media type code
c
Sound
unknown sound
Specific material designation
remote

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