The distinction between interdisciplinarity, multidisciplinarity, and transdisciplinarity is emphasized.
Chemistry evolved later as a science than physics, so that in the early 19th century renowned philosophers denied
the possibility of mathematics being useful for chemical problems. Later, with the advent of quantum mechanics,
chemistry was viewed as reducible to physics. It is argued, however, that mathematical chemistry – discrete
mathematics and graph theory – can explain chemical phenomena and concepts without the intermediacy of
physics. Isomer enumeration of cyclic and acyclic organic compounds (as molecular graphs) contributed to the
birth of graph theory. Aromatic heterocyclic compounds can be described and enumerated according to three types
of atoms forming the aromatic ring, according to the number (0, 1, or 2) of π-electrons in the non-hybridized
orbital. Benzenoids and diamondoids can be classified, described and enumerated with the help of dualists. In polycyclic benzenoids,
various π-electron partitions are possible, and among them the Clar-sextet partition is the most unequal. Topological indices that associate
numbers with molecular structures are instruments for quantitative structure-property or structure-activity relationships (QSPR and
QSAR, respectively) and drug design. Reaction graphs and synthon graphs are also mentioned. Reciprocal interaction – from chemistry
to mathematics – accounts for the discovery of new (3,g)-cages and upper/lower bounds of various energy graphs or graph connectivities.
Keywords: Benzenoids, cages, diamondoids, isomer enumeration, mathematical chemistry, molecular graphs, reaction graphs, synthon graphs.
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