DIMACS Series in
Discrete Mathematics and Theoretical Computer Science

VOLUME Fifty One
TITLE: "Discrete Mathematical Chemistry"
EDITORS: Pierre Hansen, Patrick Fowler and Maolin Zheng

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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 
    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 
    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 
    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 
    R. B. King						 235

Applications of isometric embeddings to chemical 
    S. Klavzar						 249
Geometrical and combinatorial questions about 
    J. Malkevitch					 261

Topological methods of molecular shape analysis: 
  Continuum models and discretization 
    P. G. Mezey						 267

Random networks in two dimensions. Simulations and 
    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 
    F. Zhang and H. Li					 385

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Document last modified on June 30, 2000.