Graph theory system

A connection table has been the predominant form of chemical structure representation in computer systems since the early 1980s and it is an alternative way of representing a molecular graph. Graph theory methods can equally well be applied to connection table representations of a molecule. 

Other techniques that work well on small computers are based on the molecules topology or indices from graph theory. These fields of mathematics classify and quantify systems of interconnected points, which correspond well to atoms and bonds between them. Indices can be defined to quantify whether the system is linear or has many cyclic groups or cross links. Properties can be empirically fitted to these indices. Topological and group theory indices are also combined with group additivity techniques or used as QSPR descriptors. 

A.T. Balaban, ed.. Chemical Applications of Graph Theory, Academic Press, London, 1976. V. Kvasnicka and J. Pospichal, An improved version of the constructive enumeration of molecular graphs with described sequence of valence states. Chemom. Intell. Lab. Systems, 18 (1993) 171-181. 

SMILES (Simplified Molecular Input Line Entry Systems) is a line notation system based on principles of molecular graph theory for entering and representing molecules and reactions in computer (10-13). It uses a set of simple specification rules to derive a SMILES string for a given molecular structure (or more precisely, a molecular graph). A simplified set of rules is as follows ... 

Chapter 2 describes the evolution in fundamental concepts of chemical kinetics (in particular, that of heterogeneous catalysis) and the "prehis-tory of the problem, i.e. the period before the construction of the formal kinetics apparatus. Data are presented concerning the ideal adsorbed layer model and the Horiuti-Temkin theory of steady-state reactions. In what follows (Chapter 3), an apparatus for the modern formal kinetics is represented. This is based on the qualitative theory of differential equations, linear algebra and graphs theory. Closed and open systems are discussed separately (as a rule, only for isothermal cases). We will draw the reader s attention to the two results of considerable importance. 

It is possible that in future chemists will develop concepts about a universal dynamic graph accounting for the evolution of complex chemical systems. But already graph theory can give much to chemists. In our opinion, it is quite possible that this theory will become a "chemical esperanto understandable by chemists of various specialities. 

To interpret new experimental chemical kinetic data characterized by complex dynamic behaviour (hysteresis, self-oscillations) proved to be vitally important for the adoption of new general scientific ideas. The methods of the qualitative theory of differential equations and of graph theory permitted us to perform the analysis for the effect of mechanism structures on the kinetic peculiarities of catalytic reactions [6,10,11]. This tendency will be deepened. To our mind, fast progress is to be expected in studying distributed systems. Despite the complexity of the processes observed (wave and autowave), their interpretation is ensured by a new apparatus that is both effective and simple. 

Unlike the disjoint sets of approaches to taxonomy and nomenclature for "organic chemistry" vs. "inorganic chemistry" vs. "polymer chemistry", etc., which form the cornerstone of all of the various nomenclature systems in common usage today, a common graph theory based, bi-parametric, alternating code of atoms and bonds that is equally applicable to each of these individual domains is proposed. In this system the detailed formula will be all of the name that is needed. Advantages to such an approach include ... 

As it follows from the present review, a rather complete and experimentally well-grounded quantitative theory of radical copolymerization of an arbitrary number of monomers has been developed. This theory allows one to calculate various statistical copolymers characteristics using the known values of reactivity ratios. The modern stage of the development of this theory is characterized by new approaches applying, for example, the apparatus of graph theory and theory of the dynamic systems which permit to widen the area of theoretical consideration involving the multicomponent copolymerization at high conversions. 

Graphs and electricity. After Euler the graph theory was rediscovered several times. In 1847 G. Kirchhoff developed the theory of trees to solve the problem about currents flowing in each conductor and in each loop of an electric circuit. Kirchhoff replaced the electric circuit by the graph and developed the procedure to solve the system of equations defining the current intensity, analysing only the so-called skeleton trees of the initial graph. 

Cvetkovic, D.M. and Gutman, I. (1985). The Computer System GRAPH A Useful Tool in Chemical Graph Theory. J.Comput.Chem., 7,640-644. 

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