Abstract: MATH/CHEM/COMP 2002, Dubrovnik,
June 2429, 2002

ON MODIFIED ZAGREB INDICES
Bono Lucic, Ante Milicevic, Sonja Nikolic, and Nenad Trinajstic Rudjer Boskovic Institute, POB 180,
HR10002 Zagreb, Croatia A pair of
topological indices, denoted by M1 and M2 and called Zagreb indices, have
been introduced 30 years ago^{1}. These indices found use in
the QSPR/QSAR modeling^{2}. 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 vertexdegrees and M2 index the summation of the edgeweights. We
modified these indices in the following way: the modified M1 index is the
summation of the inverse values of the (squared) vertexdegrees and the
modified M2 index is the summation of the inverse values of the
edgeweights. Modified M1 and M2 indices are formally similar to the
Randić connectivity indices of the zerothorder and firstorder. The
connectivity index of the zerothorder is given by the summation of the
square roots of the inverse values of the vertexdegrees, while the
connectivity index of the first order is given by the summation of the square
roots of the inverse values of the edgeweights. The six topological indices:
M1, M2, modified M1, modified M2, and the connectivity indices of the
zerothorder and of the firstorder are compared using the structureboiling
point models for 76 lower alkanes. ^{1} I. Gutman, N. Trinajstic, Chem. Phys. Lett. 17 (1972)
535538. ^{2} R. Todeschini, V. Consonni, Handbook of Molecular
Descriptors, WileyVCH, Weinheim, 2000. 