Topological index

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In chemical graph theory and in mathematical chemistry, a topological index is any of several numerical parameters (which are usually graph invariants) of a graph which characterize its topology. It is a kind of a molecular descriptor.[1] The Hosoya index is the first topological index recognized in chemical graph theory, and it is often referred to as "the" topological index. Another examples are the Wiener index, Randić’s molecular connectivity index, Balaban’s J index, and others.[2] Usually topological indices do not recognize double bonds and atom types (C,N,O etc.), ignore hydrogen atoms and defined for connected undirected molecular graphs only.[3]

Contents

[edit] Global and local indices

Hosoya index and Wiener index are global (integral) indices to describe entire molecule, Bonchev and Polansky introduced local (differential) index for every atom in a molecule.[3] Another examples of local indices are modifications of Hosoya index.[4]

[edit] Discrimination capability and superindices

A topological index may have the same value for a subset of different molecular graphs, i.e. the index is unable to discriminate the graphs from this subset. The discrimination capability is very important characteristic of topological index. To increase the discrimination capability a few topological indices may be combined to superindex. [5]

[edit] Computational complexity

Computational complexity is another important characteristic of topological index. The Wiener index, Randic’s molecular connectivity index, Balaban’s J index may be calculated by fast algorithms, in contrast to Hosoya index and its modifications for which non-exponentiall algorithms are unknown. [4]

[edit] References

  1. ^ Roberto Todeschini, Viviana Consonni (2000) "Handbook of Molecular Descriptors", Wiley-VCH, ISBN 3527299130
  2. ^ "Topological descriptors"
  3. ^ a b Chemical Applications of Topology and Graph Theory, ed. by R. B. King, Elsevier, 1983
  4. ^ a b Trofimov M. I., An Optimization of Procedure for Calculation of Hosoya's Index, J. Math. Chem., 1991, 8, 327.
  5. ^ Bonchev D., Mekenyan O., Trinajstić N., J. Comp. Chem., 1981, 2, 127

James Devillers, Alexandru T. Balaban (Editors), „Topological Indices and Related Descriptors in QSAR and QSPR“, Gordon and Breach (2000) Von „http://de.wikipedia.org/wiki/Topologischer_Deskriptor“

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