Topological Symmetry of Multi-shell Clusters

  • Mircea V. DiudeaEmail author
  • Atena Parvan-Moldovan
  • Fatemeh Koorepazan-Moftakhar
  • Ali Reza Ashrafi
Part of the Carbon Materials: Chemistry and Physics book series (CMCP, volume 9)


Symmetry is an intrinsic property of the organized matter. Topological symmetry is referred to the maximum possible symmetry achievable by a given molecular structure; it can be performed either by permutations on the adjacency matrix of its associate graph or by calculating the values of some topological indices. The equivalence classes of substructures of some multi-shell clusters, with icosahedral and octahedral symmetry, designed by the aid of operations on maps, were solved by using a topological index of centrality, computed on the layer matrix of rings surrounding the vertices in the molecular graph, and compared with the results of matrix permutation. A centrality order of vertices in multi-shell clusters is given. The design of multi-shell clusters was performed by our original CVNET and NanoStudio software programs.


Equivalence Class Molecular Graph Topological Index Centrality Centrality Octahedral Symmetry 
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.



The third and fourth authors are partially supported by the University of Kashan under grant no 464092/3.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Mircea V. Diudea
    • 1
    Email author
  • Atena Parvan-Moldovan
    • 1
  • Fatemeh Koorepazan-Moftakhar
    • 2
    • 3
  • Ali Reza Ashrafi
    • 2
    • 3
  1. 1.Department of Chemistry, Faculty of Chemistry and Chemical EngineeringBabes-Bolyai UniversityCluj-NapocaRomania
  2. 2.Department of Nanocomputing, Institute of Nanoscience and NanotechnologyUniversity of KashanKashanIran
  3. 3.Department of Pure Mathematics, Faculty of Mathematical SciencesUniversity of KashanKashanIran

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