Lectures and Abstracts
On the Forcing, Total Forcing, AntiForcing and AntiKekulé Numbers
Damir Vukičević
Faculty of Science, University of Split, Nikole Tesle 12, HR21000 Split
On the Zagreb Matrices
Dušanka Janežič^{1}, Sonja Nikolić^{2}, Ante Miličević^{3}, and Nenad Trinajstić^{2}
^{1}National Institute of Chemistry, Hajdrihova 19, SI1000 Ljubljana. Slovenia Email: dusa@cmm.ki.si
^{2}The Rugjer Bošković Institute, P.O.B. 180, HR10002 Zagreb, Croatia Email: sonja@irb.hr (SN); trina@irb.hr (NT)
^{3}The Institute of Medical Research and Occupational Health, P.O.B. 291, HR10002 Zagreb, Croatia Email: ante_milicevic@yahoo.com
Molecular Modeling  A New Approach
Dušanka Janežič
National Institute of Chemistry, Hajdrihova 19, 1000 Ljubljana, Slovenia
Unit distance representations of molecular graphs
Tomaž Pisanski and Boris Horvat
University of Ljubljana and University of Primorska
Molecular graphs have usually all edges of the same length. Such two or threedimensional representations
are called "unit distance representations". In this talk we study nondegenerate and degenerate unit distance
representations of some wellknown molecular graphs. In particular, we are interested in Kekule structures of such degenerate representations.
Does the Clar rule work in cyclic πelectron systems with the intramolecular hydrogen or lithium bond?
T. M. Krygowski and J. E. Zachara
Department of Chemistry, Warsaw University, Pasteura 1, 02093 Warsaw, Poland
Computing PI, Wiener and Szeged Indices of some Nanotubes and Nanotori
Ali Reza Ashrafi
Department of Mathematics, Faculty of Science, University of Kashan, Kashan, Iran
Do All Pieces Make a Whole?
Urban Bren^{1} and Matevž Bren^{2,3}
^{1}National Institute of Chemistry, Slovenia
^{2}University of Maribor, Faculty of Organizational Sciences, Slovenia
^{3}Institute of Mathematics, Physics and Mechanics, Slovenia
Detour Index of Zigzag Polyhex Nanotubes
A. Iranmanesh and Y. Pakrevesh
Department of Mathematics, Tarbiat Modarres University,
P.O.Box: 14115137, Tehran, Iran
iranmana@modares.ac.ir
Core Electrons and Hydrogen Atoms in Chemical Graph Theory
Lionello Pogliani
Dipartimento di Chimica, Universitŕ della Calabria, 87036 Rende (CS), Italy
Fax: +39.0984.492044, lionp@unical.it.
Application of the MTD Method to DyeCellulose Interactions
Simona FunarTimofei* and Ludovic Kurunczi**
* Institute of Chemistry of Timisoara, Romanian Academy,
Bul. Mihai Viteazul 24, 300223, Timisoara, Romania
email: timofei@acadicht.tm.edu.ro
** 'V. Babes' University of Medicine and Pharmacy of Timisoara,
Faculty of Pharmacy, Department of Pharmacy I,
Pta E. Murgu 2, 300034, Timisoara, Romania
Computational and theoretical results about the growth of fullerenes
Gunnar Brinkmann, Patrick Fowler, Jack Graver and Claudia Justus
In this talk we will demonstrate the interplay between computers used to explore combinatorial possibilities and suggesting theorems and mathematics proving the proposed theorems  and leading to new computations.
The example we will give is the exploration of possibilities for fullerene growth as proposed by Endo and Kroto  that is by replacing a local part of a fullerene by another part with an equal boundary structure but more Catoms.
The most important practical implication of the theoretical result we will prove is that for large fullerenes it is necessary to replace large parts in one step (instead of consecutively replacing small parts) to build them.
This shows that in nature such a process cannot occur due to an energy barrier that is too high.
Molecular Modeling  A New Approach
Dušanka Janežič
National Institute of Chemistry, Hajdrihova 19, 1000 Ljubljana, Slovenia
Topology and Electronic Structure of Nanotube Junctions of Tetrapod Shape
Kyoko Nakada, Kenji Maeda and Kota Daigoku
Department of Chemistry and Biological Science, College of Science and Engineering, Aoyama Gakuin University
Polyominoes, perfect matchings and Delannoy numbers
Peter E. John
Ilmenau, Germany
A polyomino is a connected finite plane graph without cutpoints in which all interior regions (called cells) are unit squares. Let P be a given polyomino. A simple algorithm allowed the calculation of numbers m(P) of all
perfect matchings of P. For many cases of P ( for instance: Aztec diamond) the so called called Delannoy numbers may be of interest.
The numbers m(P) play an important role in the dimer problem of statistical crystal physics.
Geometry of carbon nanotube junctions
István László
Department of Theoretical Physics, Institute of Physics and Center for Applied Mathematics and Computational Physics Budapest
University of Technology and Economics
H1521 Budapest, Hungary
Applying nanotube junctions a truly nanoelectronic architecture can be realized where both devices and interconnects are based on carbon nanotubes.
We have recently presented an algorithm for constructing junctions between single wall nanotubes of any chirality and diameter[1,2].
It is based on Geometric Intersection of Cylinders and it can describe several Y and T junctions. Using discrete manifold we developed a new and general method for the same problem.
In the present talk this method will be presented and the solutions of the corresponding diophantic equations will be discussed.
[1] I. Laszlo, Fullerenes, Nanotubes, and Carbon Nanostructures, 13, 535 (2005).
[2] I. Laszlo, Croat. Chem. Acta, 78, 217 (2005).
Basic Cluj Polynomials
Mircea V. Diudea
"BabesBolyai" University
Faculty of Chemistry and Chemical Engineering
Organic Chemistry Department
A. Janos 11 RO400028, ClujNapoca, ROMANIA
A novel class of counting polynomials, called (basic) Cluj polynomials is proposed on the ground of Cluj matrices. ^{14}
The polynomial coefficients are calculated from the above matrices or by means of orthogonal cut edges, in case of distancebased edgecalculated version.
Basic definitions and properties of the Cluj matrices and corresponding polynomials are given. Relation with other counting polynomials is evidenced.
Utility of Cluj descriptors in predicting the resonance energy of a set of planar polyhexes is exemplified.
[1] M. V. Diudea, Cluj Matrix CJu : source of various graph descriptors, Commun. Math. Comput. Chem. (MATCH), 1997, 35, 169183.
[2] M. V. Diudea, Cluj matrix invariants. J. Chem. Inf. Comput. Sci. 1997, 37, 300305.
[3] M. V. Diudea, B. Parv, and I. Gutman, DetourCluj Matrix and Derived Invariants. J. Chem. Inf. Comput. Sci. 1997, 37, 11011108.
[4] M. V. Diudea, G. Katona, I. Lukovits, and N. Trinajstić, Detour and ClujDetour Indices. Croat. Chem. Acta, 1998, 71, 459471.
The Valence Bond Matrix in Chemistry
Adrian Beteringhe^{1}, Alexandru T. Balaban^{2} and Petru Filip^{3}
^{1}Romanian Academy, "Ilie Murgulescu" Institute of Physical Chemistry, Laboratory of Supramolecular Chemistry and Interphase Processes,
Splaiul Independentei 202, 060021, Bucharest, Romania, adryan@chemist.com
^{2}Texas A&M University at Galveston, 5007 Avenue U, Galveston, TX, 77551, USA, balabana@tamug.edu
^{3}Institute of Organic Chemistry “C. D. Nenitzescu” of the Romanian Academy,
Splaiul Independentei, 202B, 060021,Bucharest, Romania, pfilip@cco.ro
A new topological index (quadratic index Q)
Adrian Beteringhe^{1}, Petru Filip^{2} and Alexandru T. Balaban^{3}
^{1}Romanian Academy, "Ilie Murgulescu" Institute of Physical Chemistry, Laboratory of Supramolecular Chemistry and Interphase Processes,
Splaiul Independentei 202, 060021, Bucharest, Romania, adryan@chemist.com
^{2}Institute of Organic Chemistry “C. D. Nenitzescu” of the Romanian Academy,
Splaiul Independentei, 202B, 060021,Bucharest, Romania, pfilip@cco.ro
^{3}Texas A&M University at Galveston, 5007 Avenue U, Galveston, TX, 77551, USA, balabana@tamug.edu
A rapid estimation of the average coreshell nanoparticle size by calcination and modeling
C. I. Lepadatu, Daniel C. Culita and Luminita Patron
Institute of Physical Chemistry “I.G.Murgulescu of Romanian Academy,
Sp. Independentei 202, Bucharest, email: costinellro@yahoo.com
Molecular descriptors for the “valence shell” of the molecule
C. I. Lepadatu
Institute of Physical Chemistry “I.G.Murgulescu of Romanian Academy,
Sp. Independentei 202, Bucharest, email: costinellro@yahoo.com
Chirotope Generation  A step towards multiconformational 3dQSA
Ralf Gugisch
University of Bayreuth, Department of Mathematics, D95440 Bayreuth, Germany
Topological Fuzzy Pharmacophore Triplets and adapted Molecular Similarity Scoring Schemes
Dragos Horvath
UMR 8576 CNRS  Université des Sciences et Technologies de Lille
Bât. C9  59655 Villeneuve d'Ascq CEDEX, France
Complexity of Alkane Isomers and their Concentration in Crude Oil
István Lukovits
Budapest, Hungary
Molecular similarity: a new similarity/diversity measure based on the partial ordering and molecular descriptors
R. Todeschini, V. Consonni, A. Mauri, D. Ballabio, M. Pavan, M.E. Cazar, and P. Tripaldi
Dept. of Environmental Sciences, University of MilanoBicocca, P.za della Scienza 1 – 20126 Milano (Italy)
Dept. of Food Science and Technologies, University of Milan, via Celoria, 2 – 20133 Milano (Italy)
Joint Research Centre, European Commission  21020 Ispra, VA (Italy)
Faculty of Science and Technology, Universidad del Azuay, Cuenca (Ecuador)
3D and 2DElectrotopological State Indices and MTD descriptor in a QSAR Study of Psychotomimetic Phenylakylamines
Maria Mracec and Mircea Mracec
Institute of Chemistry Timisoara, Romanian Academy, Bd. Mihai Viteazu 24, 300223Timisoara, Romania
Cluj and Related Polinomials Applied in QSPR Studies
A. E. Vizitiu^{a}, Mircea V. Diudea^{a} and D. Dušanka Janežič^{b}
^{a}Faculty of Chemistry and Chemical Engineering, BabesBolyai University, Arany Janos 11, 400028 Cluj, Romania
^{b}National Institute of Chemistry, Hajdrihova 19, SI1000 Ljubljana, Slovenia
3D Similarity Search on Biological Activity and other PhysicoChemical Properties of Chloramphenycol Analogues
Margareta S. Florescu^{b}, Mircea V. Diudea^{a}, Cecilia Cristea,^{c} Aniela E. Vizitiu^{a}
^{a}Faculty of Chemistry and Chemical Engineering, BabesBolyai University, Arany Janos 11, 400028 Cluj, Romania
^{b}Academy of Economic Sciences, Bucharest, Romania
^{c}University of Medicine and Pharmacy, Cluj, Romania
On Application of Directed Graphs in NMR Spectroscop
Ante Graovac^{1,2}, Drazen VikicTopic^{1}, and Damir Vukicevic^{2}
^{1}The R. Boskovic Institute, HR10002 Zagreb, POB 180, Croatia
Academy of Economic Sciences, Bucharest, Romania
^{2}Faculty of Natural Sciences, Mathematics and Kinesiology, Nikole Tesle 12,
HR21000 Split, Croatia
Szeged index – Applications for drug modeling
Prof. Vijay K. Agrawal
QSAR and Computer Chemical Laboratories,
A.P.S. University, Rewa486 003, India
Bond Currents on Double Toroids
Arnout Ceulemans^{1}, Erwin Lijnen^{1}, Mircea V. Diudea^{2}
^{1}Department of Chemistry and INPAC Institute of Nanoscale Physics and Chemistry,
Katholieke Universiteit Leuven, Celestijnenlaan 200F, B3001 Leuven, Belgium
^{2}Faculty of Chemistry and Chemical Engineering, BabeşBolyai University, Arany Janos Str. 11,
400028, ClujNapoca, Romania
