Abstract: MATH/CHEM/COMP 2002, Dubrovnik, June 24-29, 2002

ON MODIFIED ZAGREB INDICES

Bono Lucic, Ante Milicevic, Sonja Nikolic, and Nenad Trinajstic

Rudjer Boskovic Institute, POB 180, HR-10002 Zagreb, Croatia

A pair of topological indices, denoted by M1 and M2 and called Zagreb indices, have been introduced 30 years ago¹. These indices found  use in the QSPR/QSAR modeling². Since these indices in original formulation give greater weights to inner atoms and bonds, instead as one would expect to outer bonds, we modified them to conform with this expectation. In the original formulation M1 index was the summation of the squared vertex-degrees and M2 index the summation of the edge-weights. We modified these indices in the following way: the modified M1 index is the summation of the  inverse values of the (squared) vertex-degrees and the modified M2 index is the summation of the inverse values of the edge-weights. Modified M1 and M2 indices are formally similar to the Randić connectivity indices of the zeroth-order and first-order. The connectivity index of the zeroth-order is given by the summation of the square roots of the inverse values of the vertex-degrees, while the connectivity index of the first order is given by the summation of the square roots of the inverse values of the edge-weights. The six topological indices: M1, M2, modified M1, modified M2, and the connectivity indices of the zeroth-order and of the first-order are compared using the structure-boiling point models for 76 lower alkanes.

¹ I. Gutman, N. Trinajstic, Chem. Phys. Lett. 17 (1972) 535-538.

² R. Todeschini, V. Consonni, Handbook of Molecular Descriptors, Wiley-VCH, Weinheim, 2000.