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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