On the Zagreb indices as complexity indices

Nikolić, Sonja; Tolić, Iva Marija; Trinajstić, Nenad; Baučić, Ivo (2000) On the Zagreb indices as complexity indices. Croatica Chemica Acta, 73 (4). pp. 909-921. ISSN 0011-1643

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Abstract

Two original Zagreb indices, denoted M(1) and M(2), and introduced in 1972, were symmetry-modified by summing up only degrees (SMM(1)) or edge-weights (SMM(2)) 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 Nt produce exactly the same complexity ordering of nine graphs (I > H > G > F > E > D > C > B > A). The ordering produced by M(1) is different from this ordering in that it cannot discriminate E and F, and C and D. Likewise, M(2) 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 SMM(1) and SMM(2) differ considerably from orderings given by TC, TC1 and N(t) or M(2) and twc.

Item Type:	Article
Additional Information:	Rad je prezentiran na skupu Thirteenth Dubrovnik International Course and Conference MATH/CHEM/COMP'98 and the First International Dubrovnik NMR Course DU'99 NMR.
Uncontrolled Keywords:	complexity indices; molecular graphs; saturated hydrocarbons; Zagreb indices; molecular-orbitals; graph theory; index
Subjects:	NATURAL SCIENCES > Chemistry
Divisions:	Division for Marine and Enviromental Research Division of Physical Chemistry
Projects:	Project title Project leader Project code Project type Razvoj i primjena modela u kemiji Nenad Trinajstić 00980606 MZOS
Depositing User:	Nenad Trinajstić
Date Deposited:	10 Oct 2013 08:35
URI:	http://fulir.irb.hr/id/eprint/758

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