Journal of Mathematical Chemistry

, Volume 1, Issue 1, pp 61–83 | Cite as

A new approach for devising local graph invariants: Derived topological indices with low degeneracy and good correlation ability

  • P. A. Filip
  • T. -S. Balaban
  • A. T. Balaban


A new approach is presented for obtaining graph invariants which have very high discriminating ability for different vertices within a graph. These invariants are obtained as the solution set (local invariant set, LOIS) of a system of linear equationsQ · X = R, whereQ is a topological matrix derived from the adjacency matrix of the graph, andR is a column vector which encodes either a topological property (vertex degree, number of vertices in the graph, distance sum) or a chemical property (atomic number). Twenty examples of LOOIs are given and their degeneracy and ordering ability of vertices is discussed. Interestingly, in some cases the ordering of vertices obtained by means of these invariants parallels closely the ordering from an entirely different procedure based on Hierarchically Ordered Extended Connectivities which was recently reported. New topological indices are easily constructed from LOISs. Excellent correlations are obtained for the boiling points and vaporization enthalpies of alkanesversus the topological index representing the sum of local vertex invariants. Les spectacular correlations with NMR chemical shifts, liquid phase density, partial molal volumes, motor octane numbers of alkanes or cavity surface areas of alcohols emphasize, however, the potential of this approach, which remains to be developed in the near future.


Octane Partial Molal Volume Topological Index Vertex Degree Octane Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© J. C. Baltzer A. G., Scientific Publishing Company 1981

Authors and Affiliations

  • P. A. Filip
    • 1
  • T. -S. Balaban
    • 1
  • A. T. Balaban
    • 2
  1. 1.Centre of Organic ChemistryICECHIMBucharestRoumania
  2. 2.Polytechnic InstituteOrganic Chemistry DepartmentBucharestRoumania

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