Combinatorial Chemistry & High Throughput Screening - Volume 11, Issue 9, 2008

In chemistry, there is broad use of graphs and graph-theoretical invariants derived from them. Less known are directed graphs, as e.g., motivated in reaction networks. Here, the focus is on directed graphs derived from order theory. General approaches based on the structure of molecules as well as those derived from multivariate aspects in evaluation are discussed.

The periodic law, manifested in the chart of the elements, is so fundamental in chemistry and related areas of physics that the question arises “Might periodicity among molecules also be embodied in a periodic system?” This review paper details how a particular periodic system of gas-phase diatomic molecules, allowing for the forecasting of thousands of new data, was developed. It can include ionized and even quarke Read More

Combinatorial properties of graphs and groups of physico-chemical interest are described. A type of mathematical modeling is applied which involves “translating” algebraic expressions into graphs. The idea is applied to both graph theory and group theory. The former topic includes objects of importance in physics and chemistry such as trees, polyomino graphs, king boards, etc. Our study along these lines emphasiz Read More

Reaction networks are viewed as derived from ordinary molecular structures related in reactant-product pairs so as to manifest a chemical super-structure. Such super-structures then are candidates for applications in a general combinatoric chemistry. Notable additional characterization of a reaction super-structure occurs when such reaction graphs are directed, as for example when there is progressive substitution (or additi Read More

When ranking objects (like chemicals, geographical sites, river sections, etc.) by multicriteria analysis, it is in most cases controversial and difficult to find a common scale among the criteria of concern. Therefore, ideally, one should not resort to such artificial additional constraints. The theory of partially ordered sets (or posets for short) provides a solid formal framework for the ranking of objects without assigning a common s Read More

We discuss various ways in which to construct and process partial order relations or partially ordered sets (posets) in the context of ranking objects on the basis of multiple criteria. Oftentimes, it is undesirable or even impossible to devise a weighting scheme to compute a final score on the basis of the criteria. An alternative is then to restrict oneself to the information contained in the partial ordering of all objects implied by the cr Read More

Principles of partial order applied to ranking are explained. The Hasse diagram technique (HDT) is the application of partial order theory based on a data matrix. In this paper, HDT is introduced in a stepwise procedure, and some elementary theorems are exemplified. The focus is to show how the multivariate character of a data matrix is realized by HDT and in which cases one should apply other mathematical or statistical met Read More