engleski

On Zagreb Complexity Indices

The original formulation of Zagreb indices (M1 and M2) is presented and their properties are discussed. Their variants: modified ZG indices (mM1 and mM2), ZG complexity indices (TM1, TM1*, TM2 and TM2*) and the modified ZG complexity indices (mTM1, mTM1*, mTM2 and mTM2*) are presented. The modified ZG complexity indices were derived combining ideas of Bonchev1 about calculating indices for all connected subgraphs s of a graph and summing them up and using as indices the modified Zagreb indices: mTM1 =     [1/di2 (s)] (1) s vertices mTM2 =     [1/di dj(s)] (2) s edges The first sum in the above formulas represents the sum over all connected subgraphs s of a graph G. In (1), the mM1 index is calculated for each subgraph s using the vertex-degrees as they are in the graph G. If the mM1 index is calculated for each subgraph s using the vertex-degrees as they are in the isolated subgraphs, then the corresponding index is mTM1*. In the case of the mTM2 index (eq. 2), the mM2 index is calculated for each subgraph s using the edge-weights as they are in the graph G. If the mM2 index is calculated for each subgraph s using the edge-weigths as they are in the isolated subgraphs, then the corresponding index is mTM2*. The use of mTM1, mTM1*, mTM2 and mTM2* indices as complexity indices is illustrated on several classes (n-alkanes, cycloalkanes, branched acyclics, polycyclic hydrocarbons) of molecules. The use of the whole family of ZG complexitx indices in the QSPR is illustrated by modeling several properties of C3-C8 alkanes using our CROMRsel procedure. The obtained models are compared to the corresponding models in the literature.

Zagreb indices; complexity

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