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GTI-space: the space of generalized topological indices

Estrada, E. and Matamala, A.R., Ramon y Cajal program Spain (Funder) (2008) GTI-space: the space of generalized topological indices. Journal of Mathematical Chemistry, 43 (2). pp. 508-517. ISSN 0259-9791

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Abstract

A new extension of the generalized topological indices (GTI) approach is carried out to represent 'simple' and 'composite' topological indices (TIs) in an unified way. This approach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randić connectivity indices are expressed by means of the same GTI representation introduced for composite TIs such as hyper-Wiener, molecular topological index (MTI), Gutman index and reverse MTI. Using GTI-space approach we easily identify mathematical relations between some composite and simple indices, such as the relationship between hyper-Wiener and Wiener index and the relation between MTI and first Zagreb index. The relation of the GTIspace with the sub-structural cluster expansion of property/activity is also analysed and some routes for the applications of this approach to QSPR/QSAR are also given. Keywords: