Due to a detailed description of the underlying mathematical concepts and many illustrating examples the paper is well understandable, also for a non-expert. Following the traditional lines of considering homomorphic images of groups and double cosets of groups operating on sets, new methods for colouring orbits and determining automorphism groups are presented in order to construct all connected multigraphs with given degrees of vertices and forbidden or prescribed sets of subgraphs (algorithm MOLGEN).par The algorithm relies on algebraic methods rather than combinatorial considerations and allows to construct molecular graphs with given properties of considerable size and complexity, as the numerical results presented in the paper show. Thus, with MOLGEN, there is available a new successful expert system for the structural analysis of chemical compounds. Computer algebra system (CAS).

References in zbMATH (referenced in 26 articles , 1 standard article )

Showing results 1 to 20 of 26.
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  1. Rodríguez-Velázquez, Juan Alberto; Balaban, Alexandru T.: Two new topological indices based on graph adjacency matrix eigenvalues and eigenvectors (2019)
  2. Deng, Kecai; Qian, Jianguo: Enumerating stereo-isomers of tree-like polyinositols (2014)
  3. Kerber, Adalbert; Laue, Reinhard; Meringer, Markus; Rücker, Christoph; Schymanski, Emma: Mathematical chemistry and chemoinformatics. Structure generation, elucidation and quantitative structure. Property relationships (2014)
  4. Brinkmann, Gunnar; Van Cleemput, Nico; Pisanski, Tomaž: Generation of various classes of trivalent graphs (2013)
  5. Mateva, Zlatka Teneva: Constructing a canonical form of a matrix in several problems about combinatorial designs (2008)
  6. Gugisch, R.: Construction of isomorphy classes of oriented matroids (2005)
  7. Kerber, Adalbert; Laue, Reinhard; Meringer, Markus; Rücker, Christoph: Molecules in silico: potential versus known organic compounds (2005)
  8. Laue, R.; Grüner, Th.; Meringer, M.; Kerber, A.: Constrained generation of molecular graphs (2005)
  9. Kerber, A.; Laue, R.; Meringer, M.; Rücker, C.: MOLGEN-QSPR, a software package for the study of quantitative structure property relationships (2004)
  10. Brinkmann, Gunnar; Caporossi, Gilles; Hansen, Pierre: A constructive enumeration of fusenes and benzenoids. (2002)
  11. Hansen, Pierre; Mélot, Hadrien: Computers and discovery in algebraic graph theory (2002)
  12. Hässelbarth, Werner; Kerber, Adalbert: Enumeration of combinatorial libraries obtained from symmetrical parent compounds (2002)
  13. Brinkmann, Gunnar: Isomorphism rejection in structure generation programs (2000)
  14. Kerber, Adalbert: Computeralgebra and the systematic construction of finite unlabeled structures (2000)
  15. Kerber, Adalbert; Laue, Reinhard; Wieland, Thomas: Discrete mathematics for combinatorial chemistry (2000)
  16. Kerber, Adalbert; Laue, Reinhard: Group actions, double cosets, and homomorphisms: Unifying concepts for the constructive theory of discrete structures (1998)
  17. Brinkmann, G.; Steffen, E.: 3- and 4-critical graphs of small even order (1997)
  18. Grüner, Thomas; Laue, Reinhard; Meringer, Markus: Algorithms for group actions applied to graph generation (1997)
  19. Wieland, Thomas: Combinatorics of combinatorial chemistry (1997)
  20. Bangov, Ivan P.: Generation of molecular graphs based on flexible utilization of the available structural information (1996)

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