Generalization of topological indices

A generalized (molecular) graph-theoretical matrix is introduced in such a way that the adjacency and distance matrices of (molecular) graphs are particular cases of it. By using this matrix, two new molecular graph-theoretical vectors and a vector–matrix–vector multiplication procedure, a generalized invariant is introduced. This invariant permits a generalization of some of the classical topological indices (TIs). Thus, Wiener W index, Zagreb M1 and M2 indices, Balaban J index, Harary H number, Randic χ index and valence connectivity index χv resulted as particular cases of an infinite set of molecular descriptors that can be derived from the same invariant.