Graph-Theoretical Indices based on Simple, General and Complete Graphs

Valence molecular connectivity indices are based on the concept of valence delta, d v, that can be derived from general chemical graphs or chemical pseudographs. A general graph or pseudograph has multiple edges and loops and can be used to encode, through the valence delta, chemical entities. Two graph-theoretical concepts derived from chemical pseudographs are the intrinsic (I) and the electrotopological state (E) values, which are the used to define the valence delta of the pseudoconnectivity indices, ?I,S. Complete graphs encode, through a new valence delta, the core electrons of any atoms in a molecule. The connectivity indices, either valence connectivity or pseudoconnectivity, are the starting point to develop the dual connectivity indices. The dual indices show that not only can they assume negative values but also cover a wide range of numerical values. The central parameter of the molecular connectivity theory, the valence delta, defines a completely new set of connectivity indices, which can be distinguished by their configuration and advantageously used to model different properties and activities of compounds.