The development of chemical applications of graph theory is reviewed from a personal perspective. Graph-theoretical methods for finding all graphs fulfilling certain mathematical conditions followed by eliminating chemically impossible solutions are equivalent to the ‘Sherlock Holmes principle’. For molecular graphs, this is illustrated by monocyclic aromatic systems and by valence isomers of annulenes. Using dualist graphs for benzenoids and diamond hydrocarbons it was possible to develop simple encoding systems that allowed convenient enumerations of isomers. Starting with the invention of reaction (...) graphs in 1966 that included the Petersen graph which is also the 5-cage (the smallest graph with girth 5) two gaps were filled by discovering the first 10-cage and the unique 11-cage, showing how chemical clues can lead to interesting mathematical developments. Graphs of a third type are represented by synthon graphs that are helping chemical synthesis. Connections between chemical structure and molecular properties allow the design of biologically active substances on the basis of quantitative structure-activity relationships (QSARs). Some of the simplest tools for QSAR are topological indices and they are briefly discussed. (shrink)

This article discusses the nature of mathematical chemistry, discrete mathematical chemistry in particular. Molecules and macromolecules can be represented by model objects using methods of discrete mathematics, e.g., graphs and matrices. Mathematical formalisms are further applied on the model objects to distill various quantitative characteristics. The end product of such an exercise can be a better understanding of chemistry, the development of quantitative scales for qualitative notions of chemistry, or an illumination of the structural basis of chemical and biological properties. (...) The aforementioned aspects of mathematical chemistry are discussed based on my own practitioner’s perspective. (shrink)

It is pointed out that visualization, such as the structural formula of molecules, is the most important factor in ‘chemical thinking’. How mathematical chemistry has contributed to the development of mathematics is described with particular reference to the topological index or Z-index, proposed by the present author, and fullerene chemistry developed by mathematical chemists in various countries. Mathematical chemistry will be able to contribute to the development of mathematics by interplaying with mathematicians in the same way as it has been (...) developing up to the present stage. (shrink)

Mathematical chemistry entailing the development of novel mathematics for chemical applications is argued to exist, and to manifest an extremely diverse range of applications. Yet further it is argued to have a substantial history of well over a century, though the field has perhaps only attained a degree of recognition with a formal widely accepted naming in the last few decades. The evidence here for the broad range and long history is by way of numerous briefly noted example sub-areas. That (...) mathematical chemistry was only recently formally recognized is seemingly the result of its having been somewhat disguised for a period of time – sometimes because it was viewed as just an unnamed part of physical chemistry, and sometimes because the rather frequent applications in other chemical areas were not always viewed as mathematical (often involving somewhat ‘non-numerical’ mathematics). Mathematical chemistry’s relation to and distinction from computational chemistry and theoretical chemistry is further briefly addressed. (shrink)

We first show some successes of discrete mathematical chemistry (DMC), a branch of theoretical chemistry born in the 1960s and 1970s. Then we explore the social context in which the emergence of DMC took place, initiated mainly in East European countries. The availability of knowledge, especially of mathematical knowledge, and the lack of research funds were the main conditions that helped get DMC started. We also explore the reception of DMC in the chemical and mathematical circles, being flat rejection in (...) chemistry and slow acceptance in mathematics. Finally, we discuss some definitions of the subject and propose a new one stating that mathematical chemistry is the realization of mathematical thinking in chemistry, understood as functional thinking defined by Felix Klein in the Erlangen Program. (shrink)