ABSTRACT
TOPOLOGICAL INDICES A single number that can be used to characterize the graph of a molecule
is called a topological index,^ (The term graph-theoretical index would be more accurate than topological index, but the latter is more common in the chemical literature.) A topological index, thus, appears to be a convenient device for converting chemical constitution into a number. Evidently, this number must have the same value for a given molecule regardless of ways in which the corresponding graph is drawn or labeled. Such a number is referred to by graph theorists as a graph invariant (see Chapter 2, Section II). For example, one of the simplest graph invariants (topological indices) is the number of vertices in the graph (the number of atoms in the molecule). Hence, it could be simply said that topological indices are graph invariants. It should also be pointed out that topological indices do not generally allow the reconstruction of the molecular graph, implying that a certain loss of information has occurred during their creation.
