Hypergraph models of hydrocarbon molecules and their applications in computer chemistry

A new form of representing the structures of saturated hydrocarbons as hypergraphs of special kind is suggested. A vertex of such hypergraph corresponds to a carbon atom in the molecule, and a hyperedge is defined as a set of vertices corresponding to some fixed carbon atom and all carbon atoms bounded with it. The comparison of the traditional graph model and the suggested hypergraph model using definite quantitative criteria related to some tasks of computer chemistry is fulfilled. For these investigations some set of hydrocarbons presented by their structural formulae is used. In particular, different invariants and codes of graphs and hypergraphs were calculated and their degeneration on the given set of structures was studied and compared. Two models were also compared by the ability of some local vertex invariants derived from them to distinguish topologically nonequivalent vertices in the traditional graph model. It is shown that in all cases in accordance with the used criteria the hypergraph model is better than the graph model. Besides, a number of structure–property relationships on the base of invariants of the suggested hypergraphs was obtained

hypergraph, graph invariants, hypergraph invariants, computer chemistry, structure–property relationships, saturated hydrocarbons.

1. www.ru.wikipedia.org/wiki/компьютерная_химия

2. Соловьев М.Е., Соловьев М.М. Компьютерная химия. М.: СОЛОН-Пресс, 2005. 536 с.

3. www.newsru.com/world/09oct2013/nobel.htlm

4. Станкевич М.И., Станкевич И.В., Зефиров Н.С. Топологические индексы в органической химии // Успехи химии. 1988. Т. 57. № 3. С. 337-366.

5. Константинова Е.В. Графы, гиперграфы и их инварианты для характеризации молекулярных структур: дис.. канд. техн. наук. Новосибирск: РАН. Сиб. отд-ние. Новосибирский ин-т орган. химии, 1992. 198 с.

6. Stankevich I.V., Gal’pern E.G., Chistyakov A.L., Baskin I.I., Skvortsova M.I., Zefirov N.S., Tomilin O.B. Spectral theory of graphs in chemistry. 1. Projection operators and canonical numeration of graph vertices // J. Chem. Inform. & Computer Sci. 1994. V. 34. № 5. P. 1105-1108.

7. Stankevitch M.I., Tratch S.S., Zefirov N.S. Combinatorial models and algorithms in chemistry. Search for isomorphisms and automorphisms of molecular graphs // J. Comput. Chem. 1988. V. 9. № 4. P. 303-320.

8. Емеличев В.А., Мельников О.И., Сарванов В.И., Тышкевич Р.И. Лекции по теории графов : учеб. пособие. М.: ЛИБРОКОМ, 2009. 392 с.

9. Konstantinova E.V., Skorobogatov V.A. Molecular hypergraphs: the new representation of nonclassical molecular structures with polycentric delocalized bonds // J. Chem. Inform. & Computer Sci. 1995. V. 35. № 3. P. 472-473.

10. Konstantinova E.V., Skorobogatov V.A. Application of hypergraph theory in chemistry // Discrete Mathematics. 2001. V. 235. P. 365-383.

11. Skvortsova M.I., Fedyaev K.S., Palyulin V.A., Zefirov N.S. Molecular design of chemical compounds with prescribed properties from QSAR models containing the Hosoya index // Internet Electronic Journal of Molecular Design. 2003. V. 2. № 2. P.70-85.