ГИПЕРГРАФОВЫЕ МОДЕЛИ МОЛЕКУЛ УГЛЕВОДОРОДОВ И ИХ ПРИМЕНЕНИЕ В КОМПЬЮТЕРНОЙ ХИМИИ

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 obtainedПредложен новый способ представления структур насыщенных углеводородов в виде гипер-графов специальной конструкции. Проведено сравнение традиционной графовой модели и предложенной гиперграфовой модели. Для этой цели введен ряд количественных критериев, характеризующих эффективность применения той или иной модели при решении опре-деленных задач компьютерной химии. Для исследований использована некоторая выборка угле-водородов, представленных своими структурными формулами. Показано, что по всем рассмотренным критериям гиперграфовая модель превосходит графовую. Кроме того, на основе инвариантов предложенных гиперграфов для соединений заданной выборки построен ряд корреляций «структура-свойство»

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 obtaine