A generalized graph-theoretical matrix of heterosystems and its application to the VMV procedure

The extensions of generalized (molecular) graph-theoretical matrix and vector–matrix–vector procedure are considered. The elements of the generalized matrix are redefined in order to describe molecules containing heteroatoms and multiple bonds. The adjacency, distance, detour and reciprocal distance matrices of heterosystems, and corresponding vectors are derived from newly defined generalized graph matrix. The topological indices, which are most widely used in predicting physicochemical and biological properties/activities of various compounds, can be calculated from the new generalized vector–matrix–vector invariant.

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► The generalized (molecular) graph-theoretical matrix of heterosystems is defined.
► The VMV procedure is generalized to heterosystems.
► The VMV procedure is extended to new relations.