Background for Molecular Connectivity

The approach used in chemical graph theory is to abstract from the molecular structure those elements that lead to structure variables in the form of numerical indexes. The set of atoms and connections is viewed as structure information but in a form not amenable directly to QSAR analysis. The first step is to adopt a form for the molecular skeleton as the basis for extraction of structure information. To represent the molecular skeleton, the hydrogen-suppressed graph is most commonly used hydrogen atoms are not explicitly considered hydrogen atoms are incorporated in skeletal groups which are the graph vertexes. 

The lowest level structure descriptor is simply the count of atoms. However, only in alkanes are the properties even roughly proportional to the number of atoms. More information-rich structure indicators are needed. In the earliest topological methods, numerical indexes were developed simply by counting the number of edges or pairs of adjacent edges. Wiener,Platt,and others developed structure indexes that produced interesting correlations to some properties of saturated hydrocarbons. As impressive as this work is, it could not be readily or usefully extended to unsaturated compounds or to heteroatom- 

This development is appropriate only for saturated alkanes - - because there is no provision for atom identity, bond types, or number of hydrogen atoms in each skeletal group (except for the case of saturated hydrocarbons.) This branching index is essentially a mathematical property of graphs it does not adequately represent molecular graphs. Further, a single index would appear to be insufficient to relate to the wide variety of molecular properties, especially when biological and environmental properties are of interest. 

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