Springer Science+Business Media B.V., 2011. — 304 p. — (Carbon Materials: Chemistry and Physics 4) — ISBN: 9789400702202This book has been conceived during the 24th MATH/CHEM/COMP MCC Conference in Dubrovnik, placed along the beautiful and inspiring coast of Croatia in June 2009, and involves some of the most authoritative experts in this elegant field of nanoscience, placed at the border between mathematics and chemistry. Since their discovery, fullerenes molecules are intimately connected to mathematics. Geometry, topology, number theory and other mathematical instruments greatly assist researchers to classify fullerenes structures and to predict their unique physical and chemical properties. The name itself of these hollow molecules of pure carbon is rooted in geometry, homage to Richard Buckminster Fuller and to his geodesic dome, the inspiring structure of the “buckminsterfullerene” C 60 discovered by Robert Curl, Harold Kroto and Richard Smalley in 1985. This epochal, and in somehow epical, discovery has been awarder by 1996 Nobel Prize for Chemistry. The amplitude of the topics and the level of the contributions are prominent characters of this scientific book that will help researchers in studying and understanding fullerenes properties. For this, we are fully indebted with all authors for their competent and patient works and with Prof. Harold Kroto for his introduction to this monograph that, in many pages, shows that beauty is present in science. We would also like to thank Springer for the opportunity to publish this book and Springer people who allowed all our efforts to become a real text. Contents Omega Polynomials of Fullerenes and Nanotubes Wiener Index of Nanotubes, Toroidal Fullerenes and Nanostars C60 Structural Relatives – An Omega-Aided Topological Study Local Combinatorial Characterization of Fullerenes Computation of Some Topological Indices of C60 and C80 Fullerenes by GAP Program 4-Regular and Self-Dual Analogs of Fullerenes Endohedral Fullerene Complexes and In-Out Isomerism in Perhydrogenated Fullerenes Detailed Atlas of Kekulé Structures of the Buckminsterfullerene A Graph Theoretic Approach to Atomic Displacements in Fullerenes Counting Spanning Trees in Toroidal Fullerenes Topological Determination of 13C–NMR Spectra of C66 Fullerenes The Topological Background of Schwarzite Physics High π-Electronic Stability of Soccer Ball Fullerene C60 and Truncated Octahedron C24 Among Spherically Polyhedral Networks The Estrada Index and Fullerene Isomerism
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