Symmetry and Complexity

  • Mircea Vasile Diudea
Part of the Carbon Materials: Chemistry and Physics book series (CMCP, volume 10)


Classical geometric symmetry refers to some operations acting on geometric properties of a polyhedron, that leave the object invariant; it is reflected in several molecular properties, such as dipole moments, IR vibrations, 13C-NMR signals etc. Topological symmetry, defined in terms of connectivity, is addressed to constitutive aspects of a molecule and it is involved in synthesis and/or structure elucidation. Complexity refers to the state or quality of being complex/intricate/complicated, or being the union of some interacting (by some rules) parts. Structural complexity is addressed to the organization of matter. It is studied by the aid of graphs associated to molecules/ions/crystals, on which basis several descriptors are calculated. Topological symmetry speaks about structural complexity by considering the type of atoms/vertices and their reciprocal distribution. Genus and rank (or space dimension) of a structure are parameters of complexity acting by means of Euler characteristic of the embedding surface. The fourth chapter introduces to: Euler characteristic, topological symmetry, indices of centrality, ring signature index and Euler characteristic, as reflected in pairs of map operations.


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© Springer International Publishing AG 2018

Authors and Affiliations

  • Mircea Vasile Diudea
    • 1
  1. 1.Department of Chemistry, Faculty of Chemistry and Chemical EngineeringBabes-Bolyai UniversityCluj-NapocaRomania

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