ABSTRACT
At this pdn t in our narrative, we pause to gain the high ground con cerning the development of chemical graph theory as a whole. Following the major turbulence of the 1850s and 1860s, generated by the advent of structure and valence theories, the need for appropriate mathematical for malisms for the farther development of chemistry became clear. Graph theory represented a very natural formalism for chemistry and had al ready been employed in a variety of implicit guises. Over the succeeding years the use of graph theory in chemistry was to assume an increasingly explicit form. The applications began to multiply so fast that chemical graph theory bifurcated in manifold ways to evolve into an assortment of different specialisms. Coverage of all the ramifications would result in a chapter of unmanageable proportions, and so some narrowing of our focus of interest is essential from here on. To maintain as broad an overview as posfflble, we shall feature four key areas of the development of chemi cal graph theory. In the following four sections, we discuss the topics of isomer enumeration, additivity studies, topolopcal indices, and chemical bonding theory. -
In general, it may be commented that the development of chenxical graph theory has not been a particularly smooth one. Indeed, it can be said, that periods of great interest in the field have been followed by almost total ne^ect. The episodic nature of the interest by chemists has refiected to a large extent the themes of current chemical interest at the time. Thus, in the 1930s, many chemists were involved in the synthesis of a whole range of new types of molecules, and so determining the number of possible structures which could be made theoretically became of some significance. It was daring the 1930s that isomer enumeration studies had their heyday. Chemical bonding theory had been a topic of perennial interest, though the topological nature of simple bonding theory began to be realized only in the late 1950s. As a consequence, in
the period immediately fdlowing, an explosion occurred in the number of papers treating the subject of bonding theory from a graph-theoretical standpoint. In very recent times, in the 1970s and 1980s, chemical graph theory seems to have become broadly fashionable again, even among a fair number of mathematicians.
