### Abstract

A new extension of the generalized topological indices (GTI) approach is carried out torepresent 'simple' and 'composite' topological indices (TIs) in an unified way. Thisapproach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randićconnectivity indices are expressed by means of the same GTI representation introduced for composite TIs such as hyper-Wiener, molecular topological index (MTI), Gutman index andreverse 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 GTI space 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.

Original language | English |
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Pages (from-to) | 508-517 |

Number of pages | 9 |

Journal | Journal of Mathematical Chemistry |

Volume | 43 |

Issue number | 2 |

DOIs | |

Publication status | Published - 28 Feb 2008 |

### Keywords

- graph theory
- generalized graph matrix
- topological indices
- molecular descriptors
- algebraic graph theory

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## Cite this

Estrada, E., Matamala, A. R., & Ramon y Cajal program Spain (Funder) (2008). GTI-space: the space of generalized topological indices.

*Journal of Mathematical Chemistry*,*43*(2), 508-517. https://doi.org/10.1007/s10910-006-9211-9