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Topological Complexity of Molecules

The concept of complexity has intrigued people from the beginning of history, but only in our times have attempts to quantify it begun to appear with a new science emerging – the science of complexity. Manifestation of complexity can be found everywhere in nature and life (Waldrop 1992), and different levels of complexity are encountered in arts, humanities, and sciences (Rouvray 2003). Like many concepts in chemistry, the concept of complexity appears to be a fuzzy but useful concept (Rouvray 1997). The fuzziness of this concept has not prevented chemists from attempting to quantify it (Nikolić et al. 2003). Here we are concerned with topological complexity of molecules. It should be stated at the outset that there are different levels of complexity regarding the structure of molecules (Bonchev and Seitz 1997), i.e., elemental or compositional or 1-dimensional complexity (which is determined by the partition of a graph’s vertices into classes of different types), topological or 2-dimensional complexity, and dynamical or 3-dimensional complexity (a complexity feature of fluctuating molecules). The topological complexity index will be abbreviated as TCI, and this symbol will be used throughout the entry.

Complexity, Molecular graph, Topological complexity,

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