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This volume contains the proceedings from the first DIMACS meeting on discrete mathematical chemistry held at Rutgers University (New Brunswick, NJ). The contributions reflect the presentations and spotlight the breadth of current research on the topic--from the Benzenoid Clar problem to the Wulff-shape of sphere packings. Much of the volume reflects the combined mathematical and physical interest in the new molecules, fullerenes.
This DIMACS conference highlighted the range of opportunities for fruitful and informed collaboration across the mathematics-chemistry boundaries. The interdisciplinary nature of the contributions pays testament to the fact that "real" chemistry and "real" mathematics do indeed interact.
Participants xi
Contributing Authors xiii
Foreword xv
Preface xvii
Dedication xix
The Clar and Fries problems for benzenoid
hydrocarbons are linear programs
H. Abeledo and G. Atkinson 1
Use of graph invariants in QMSA and predictive
toxicology
S. C. Basak and B. D. Gute 9
Isomorphism rejection in structure generation programs
G. Brinkmann 25
Foldedness in linear polymers: A difference between
graphical and Euclidean distances
L. Bytautas, D. J. Klein, M. Randic,
and T. Pisanski 39
Enumeration of fusenes to h = 20
G. Caporossi, P. Hansen, and M. Zheng 63
Characterizing properties of some graph invariants
related to electron charges in the Huckel molecular
orbital theory
D. Cvetkovic 79
Fast embeddings for planar molecular graphs
O. D. Friedrichs 85
More icosahedral fulleroids
O. D. Friedrichs and M. Deza 97
Representation of stereochemistry using combinatorial
maps
A. Dietz, C. Fiorio, M. Habib, and C. Laurenco 117
Geometric symmetry and chemical equivalence
B. T. Fan, A. Panaye, J. H. Yao, S. G. Yuan,
and J. P. Doucet 129
(3-6)-cages, hexagonal toroidal cages, and their
spectra
P. W. Fowler, P. E. John, and H. Sachs 139
A generalized ring spiral algorithm for coding
fullerenes and other cubic polyhedra
P. W. Fowler, T. Pisanski, A. Graovac,
and J. Zerovnik 175
An efficient algorithm for determining fixed bonds
and normal components in a bipartite graph
X. Guo and M. Randic 189
Numerical solutions of the Laplace equation in
chemical spaces
R. Hefferlin 199
Chemical frameworks and hyperbolic tilings
S. T. Hyde and S. Ramsden 203
Discrete mathematics for combinatorial chemistry
A. Kerber, R. Laue, and T. Wieland 225
Carbon networks on cubic infinite periodic minimal
surfaces
R. B. King 235
Applications of isometric embeddings to chemical
graphs
S. Klavzar 249
Geometrical and combinatorial questions about
fullerenes
J. Malkevitch 261
Topological methods of molecular shape analysis:
Continuum models and discretization
P. G. Mezey 267
Random networks in two dimensions. Simulations and
correlations
H. M. Ohlenbusch, N. Rivier, T. Aste,
and B. Dubertret 279
Group and graph theoretical perspectives on the
structures of large icosahedral cages
C. M. Quinn, D. B. Redmond, and P. W. Fowler 293
Use of path matrices for a characterization of
molecular structures
M. Randic, X. Guo, and S. Bobst 305
Star sets and star complements in finite graphs:
A spectral construction technique
P. Rowlinson 323
Geometry and energetics of high genus fullerenes
and nanotubes
H. Terrones and M. Terrones 333
An abstract representation for molecular graphs
P. Vismara and C. Laurenco 343
The Wulff-shape of large periodic sphere packings
J. M. Wills 367
On hypercycles and hypercircuits in hypergraphs
A. V. Zeigarnik 377
On maximal energy ordering of acyclic conjugated
molecules
F. Zhang and H. Li 385
Index of Volumes
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