Graph theoretical analysis, mathematical

Randic M, Wilkins CL (1980) Graph Theoretical Analysis of Molecular Properties Isomeric Variation in nonanes. Int J Quant Chem 18 1005-1027 Rosen KH (1991) Discrete Mathematics and its Applications. McGraw-Hill, Inc, New York, p 391... 

Ohkami N, Motoyama A, Yamaguchi T, Hosoya H, Gutman I (1981) Graph—Theoretical Analysis of the Clar s Aromatic Sextet — Mathematical Pro rties of the Set of the Kekule Patterns and the Sextet Polynomial for Polycyclic Aromatic Hydrocarbons. Tetrahedron 37 1113... 

When considering expansions, some caution has to be exercised in allowing for a possibility that an apparently different form of an expansion may turn out to be mathematically equivalent. This has already been seen with Herndon s resonance theory and the conjugated circuits method, which can both lead to the same expressions for the molecular resonance energy. The distinction between such expansions may be in the interpretation of the terms used. This is well illustrated with a comparison of the quantum chemically computed diamagnetic susceptibilities of alkanes and the graph theoretical analysis of the same diamagnetic susceptibilities briefly outlined below. 

Mathematical chemistry, the new challenging discipline of chemistry has established itself in recent years. Its main goal is to develop formal (mathematical) methods for chemical theory and (to some extent) for data analysis. Its history may be traced back to Caley s attempt, more than 100 years ago, to use the graph theoretical representation and interpretation of the chemical constitution of molecules for the enumeration of acyclic chemical structures. Graph theory and related areas of discrete mathematics are the main tools of qualitative theoretical treatment of chemistry [1,2]. However, attempts to contemplate connections between mathematics and chemistry and to predict new chemical facts with the help of formal mathematics have been scarce throughout the entire history of chemistry. 

One can immediately see the advantage of mathematical (graph-theoretical) techniques over quantum-chemical calculations in fields, which requires analysis of structure-property relation (such as environmental sciences). We quote the following paragraph from a paper by Randic et al. (1985). 

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