Substructure, Subgraph, and Walk Counts as Measures of the Complexity of Graphs and Molecules

Journal of Chemical Information and Computer Sciences

Volumn 41, Issue 6, 2001, Pages 1457-1462

  Rücker, Gerta ^a   Rücker, Christoph ^a  

^a UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE;

WALK COUNTS;

CHEMICAL BONDS; COMPUTER PROGRAMMING; MOLECULAR GRAPHICS; MOLECULAR STRUCTURE;

AROMATIC COMPOUNDS;

EID: 0035526172     PISSN: 00952338     EISSN: None     Source Type: Journal    
DOI: 10.1021/ci0100548     Document Type: Article

References (34)

1. Bertz, S. H.; Herndon, W. C. The Similarity of Graphs and Molecules. In Artificial Intelligence Applications in Chemistry; Pierce, T. H., Hohne, B. A., Eds.; American Chemical Society: Washington, DC, 1986; pp 169-175.
2. Bertz, S. H.; Sommer, T. J. Rigorous Mathematical Approaches to Strategic Bonds and Synthetic Analysis Based on Conceptually Simple New Complexity Indices. Chem. Commun. 1997, 2409-2410.
3. Bertz, S. H.; Wright, W. F. The Graph Theory Approach to Synthetic Analysis: Definition and Application of Molecular Complexity and Synthetic Complexity. Graph Theory Notes of New York 1998, 35, 32-48.
4. Bertz, S. H.; Zamfirescu, C. M. New Complexity Indices Based on Edge Covers. MATCH - Commun. Math. Comput. Chem. 2000, 42, 39-70.
5. Bertz, S. H. Complexity of Molecules and Their Synthesis. A chapter in ref 18.
6. Bonchev, D. Novel Indices for the Topological Complexity of Molecules. SAR QSAR Environ. Res. 1997, 7, 23-43.
7. (a) Bonchev, D. Overall Connectivity and Topological Complexity: A New Tool for QSPR/QSAR. In Topological Indices and Related Descriptors in QSAR and QSPR; Devillers, J., Balaban, A. T., Eds.; Gordon & Breach: Reading, U.K., 1999; pp 361-401.
8. (b) Bonchev, D. Overall Connectivities/Topological Complexities: A New Powerful Tool for QSPR/QSAR. J. Chem. Inf. Comput. Sci. 2000, 40, 934-941.
9. Bonchev, D.; Gordeeva, E. Hierarchical Partially Ordered Sets Based on Topological Complexity. MATCH - Commun. Math. Comput. Chem. 2000, 42, 85-117.
10. Bonchev, D.; Trinajstić, N. Overall Molecular Descriptors. 3. Overall Zagreb Indices. SAR QSAR Environ. Res. 2001, 12, 213-236.
11. Bonchev, D. The Overall Wiener Index - A New Tool for Characterisation of Molecular Topology. J. Chem. Inf. Comput. Sci. 2001, 41, 582-592.
12. Bonchev, D. Overall Connectivity - A Next Generation Molecular Connectivity. J. Mol. Graphics Modell. 2001, 20, 65-75.
13. Bone, R. G. A.; Villar, H. O. Exhaustive Enumeration of Molecular Substructures. J. Comput. Chem. 1997, 18, 86-107.
14. Rücker, G.; Rücker, C. Automatic Enumeration of All Connected Subgraphs. MATCH - Commun. Math. Comput. Chem. 2000, 41, 145-149.
15. Rücker, G.; Rücker, C. On Finding Nonisomorphic Connected Subgraphs and Distinct Molecular Substructures. J. Chem. Inf. Comput. Sci. 2001, 41, 314-320, 865.
16. Rücker, G.; Rücker, C. Counts of All Walks as Atomic and Molecular Descriptors. J. Chem. Inf. Comput. Sci. 1993, 33, 683-695.
17. Rücker, G.; Rücker, C. Walk Counts, Labyrinthicity, and Complexity of Acyclic and Cyclic Graphs and Molecules. J. Chem. Inf. Comput. Sci. 2000, 40, 99-106.
18. Nevertheless, usually the graph itself (the structure itself) is also included in the set of its subgraphs (substructures). We follow this practice here.
19. Complexity in Chemistry (Mathematical Chemistry Series; Bonchev, D., Rouvray, D. H., Eds.; Taylor & Francis: Reading, U.K., Vol. 7, in press.
20. Nikolić, S.; Trinajstić, N.; Tolić, I. M.; Rücker, G.; Rücker, G.; On Molecular Complexity Indices. A chapter in ref 18.
21. Nikolić, S.; Tolić, I. M.; Trinajstić, N. On the Complexity of Molecular Graphs. MATCH - Commun. Math. Comput. Chem. 1999, 40, 187-201.
22. Nikolić, S.; Tolić, I. M.; Trinajstić, N.; Baucić, I. On the Zagreb Indices as Complexity Indices. Croat. Chem. Acta 2000, 73, 909-921.
23. Randić, M. On the Concept of Molecular Complexity. Croat. Chem. Acta, in press.
24. 7a,b
25. Structure 6 is shown here only to demonstrate the effect; it is not implied that 6 is capable of existence as a real compound.
26. A so-called substructure search in the CAS Registry File or in Beilstein Crossfire (which could more correctly be called a superstructure search) performed on an alcohol query will not retrieve the corresponding carbonyl compound, nor will a nitrile be retrieved as a result of such a search on a primary amine or inline query.
27. For example, any alkene has as one of its substructures ethene, which gives rise to two kinds of subgraphs, ethene and ethane. The latter is found in most organic compounds anyway.
28. Gutman, I.; Rücker, C.; Rücker, G. On Walks in Molecular Graphs. J. Chem. Inf. Comput. Sci. 2001, 41, 739-745.
29. (a) Rücker, G.; Rücker, C. Computer Perception of Constitutional (Topological) Symmetry: TOPSYM, a Fast Algorithm for Partitioning Atoms and Pairwise Relations among Atoms into Equivalence Classes. J. Chem. Inf. Comput. Sci. 1990, 30, 187-191.
30. (b) Rücker, G.; Rücker, C. Isocodal and Isospectral Points, Edges, and Pairs in Graphs and How to Cope with Them in Computerized Symmetry Recognition. J. Chem. Inf. Comput. Sci. 1991, 31, 422-427.
31. (a) Bertz, S. H. A Mathematical Model of Molecular Complexity. In Chemical Applications of Topology and Graph Theory; King, R. B., Ed.; Elsevier: New York, 1983; pp 206-221.
32. (b) Bertz, S. H.; Sommer, T. J. Application of Graph Theory to Synthesis Planning: Complexity, Reflexivity, and Vulnerability. In Organic Synthesis: Theory and Applications; Hudlicky, T., Ed.; JAI Press: Greenwich, CT, 1993; Vol. 2. pp 67-92.
33. (a) Whitlock, H. W. On the Structure of Total Synthesis of Complex Natural Products. J. Org. Chem. 1998, 63, 7982-7989.
34. (b) Barone, R.; Chanon, M. A New and Simple Approach to Chemical Complexity, Application to the Synthesis of Natural Products. J. Chem. Inf. Comput. Sci. 2001, 41, 269-272.