Exploring the Limits of Graph Invariant- and Spectrum-Based Discrimination of (Sub)structures

The limits of a recently proposed computer method for finding all distinct substructures of a chemical structure are systematically explored within comprehensive graph samples which serve as supersets of the graphs corresponding to saturated hydrocarbons, both acyclic (up to n = 20) and (poly)cyclic (up to n = 10). Several pairs of smallest graphs and compounds are identified that cannot be distinguished using selected combinations of invariants such as combinations of Balaban's index J and graph matrix eigenvalues. As the most important result, it can now be stated that the computer program NIMSG, using J and distance eigenvalues, is safe within the domain of mono- through tetracyclic saturated hydrocarbon substructures up to n = 10 (oligocyclic decanes) and of all acyclic alkane substructures up to n = 19 (nonadecanes), i.e., it will not miss any of these substructures. For the regions surrounding this safe domain, upper limits are found for the numbers of substructures that may be lost in the worst case, and these are low. This taken together means that the computer program can be reasonably employed in chemistry whenever one is interested in finding the saturated hydrocarbon substructures. As to unsaturated and heteroatom containing substructures, there are reasons to conjecture that the method's resolving power for them is similar.

[1]  Ernö Pretsch,et al.  Automated Compatibility Tests of the Molecular Formulas or Structures of Organic Compounds with Their Mass Spectra , 1999, J. Chem. Inf. Comput. Sci..

[2]  Kurt Varmuza,et al.  Maximum Common Substructures of Organic Compounds Exhibiting Similar Infrared Spectra. , 1998 .

[3]  Neil Immerman,et al.  An optimal lower bound on the number of variables for graph identification , 1992, Comb..

[4]  Edwin R. Hancock,et al.  Eigenspaces for Graphs , 2002, Int. J. Image Graph..

[5]  D. Cvetkovic,et al.  Eigenspaces of graphs: Bibliography , 1997 .

[6]  Haruo Hosoya,et al.  Topological Twin Graphs. Smallest Pair of Isospectral Polyhedral Graphs with Eight Vertices , 1994, J. Chem. Inf. Comput. Sci..

[7]  Frank Harary,et al.  The Characteristic Polyomial Does Not Uniquely Determine the Topology of a Molecule , 1971 .

[8]  Marjan Vračko,et al.  Eigenvalues as Molecular Descriptors , 2001 .

[9]  Dejan Plavšić,et al.  The distance matrix in chemistry , 1992 .

[10]  A. Balaban.  Highly discriminating distance-based topological index , 1982 .

[11]  F. Harary.  New directions in the theory of graphs , 1973 .

[12]  Nenad Trinajstić,et al.  Isomer discrimination by topological information approach , 1981 .

[13]  Gerta Rücker,et al.  Substructure, Subgraph, and Walk Counts as Measures of the Complexity of Graphs and Molecules , 2001, J. Chem. Inf. Comput. Sci..

[14]  Danail Bonchev,et al.  The Overall Wiener Index-A New Tool for Characterization of Molecular Topology , 2001, J. Chem. Inf. Comput. Sci..

[15]  Kurt Varmuza,et al.  Substructure Isomorphism Matrix , 2000, J. Chem. Inf. Comput. Sci..

[16]  M. Elyashberg,et al.  An expert system for automated structure elucidation utilizing 1H-1H, 13C-1H and 15N-1H 2D NMR correlations , 2001, Fresenius' journal of analytical chemistry.

[17]  B. Weisfeiler.  On construction and identification of graphs , 1976 .

[18]  Vladimir Poroikov,et al.  Robustness of Biological Activity Spectra Predicting by Computer Program PASS for Noncongeneric Sets of Chemical Compounds , 2000, J. Chem. Inf. Comput. Sci..

[19]  Robin J. Wilson,et al.  An Atlas of Graphs , 1999 .

[20]  Kurt Varmuza,et al.  Maximum Common Substructures of Organic Compounds Exhibiting Similar Infrared Spectra , 1998, J. Chem. Inf. Comput. Sci..

[21]  Marko Razinger,et al.  Structural selectivity of topological indexes in alkane series , 1985, J. Chem. Inf. Comput. Sci..

[22]  Subhash C. Basak,et al.  Characterization of Isospectral Graphs Using Graph Invariants and Derived Orthogonal Parameters , 1998, J. Chem. Inf. Comput. Sci..

[23]  Gerta Rücker,et al.  On Finding Nonisomorphic Connected Subgraphs and Distinct Molecular Substructures , 2001, J. Chem. Inf. Comput. Sci..

[24]  S. S. Shrikhande.  On a Characterization of the Triangular Association Scheme , 1959 .