Reminescences

On the Zagreb Indices as Complexity Indices

Sonja Nikolić orcid.org/0000-0003-3203-040X ; The Rugjer Bošković Institute, P. O. Box 180, HR-10002 Zagreb, Croatia
Iva Marija Tolić ; The Rugjer Bošković Institute, P. O. Box 180, HR-10002 Zagreb, Croatia
Nenad Trinajstić ; The Rugjer Bošković Institute, P. O. Box 180, HR-10002 Zagreb, Croatia
Ivo Baučić ; Department of Fixed Prosthodontics, Faculty of Stomatology, University of Zagreb, HR-10001 Zagreb, Croatia

Abstract

Two original Zagreb indices, denoted M₁ and M₂, and introduced in 1972, were symmetry-modified by summing up only degrees (SMM₁) or edge-weights (SMM₂) of symmetry nonequivalent vertices or edges of graphs. Their dependence on the structural features and symmetry of molecular graphs is studied. They were also compared to eight other complexity indices (RCI, TC, TC1, BT, BI, twc, wcx) on nine graphs (A, B, C, D, E, F, G, H, I) with five vertices that were earlier studied by several research groups. The TC, TC1 and N_t produce exactly the same complexity ordering of nine graphs (I>H>G>F>E>D>C>B>A). The ordering produced by M1 is different from this ordering in that it cannot discriminate E and F, and C and D. Likewise, M₂ and twc produce exactly the same ordering and the latter ordering differs from the former only in the reverse order of E and F. Orderings produced by SMM₁ and SMM₂ differ considerably from orderings given by TC, TC1 and N_t or M₂ and twc.

Keywords

complexity indices; molecular graphs; saturated hydro-carbons; Zagreb indices

Hrčak ID:

131967

URI

https://hrcak.srce.hr/131967

Publication date:

4.12.2000.

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