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Distance, Symmetry, and Topology in Carbon Nanomaterials pp 61–82Cite as

Topological Symmetry of Multi-shell Clusters

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Part of the book series: Carbon Materials: Chemistry and Physics ((CMCP,volume 9))

Abstract

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.

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Acknowledgment

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

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Authors and Affiliations

  1. Department of Chemistry, Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, Arany Janos Street 11, Cluj-Napoca, RO-400028, Romania

    Mircea V. Diudea & Atena Parvan-Moldovan

  2. Department of Nanocomputing, Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan, 87317-53153, Iran

    Fatemeh Koorepazan-Moftakhar & Ali Reza Ashrafi

  3. Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, 87317-53153, Iran

    Fatemeh Koorepazan-Moftakhar & Ali Reza Ashrafi

Authors
  1. Mircea V. Diudea
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  2. Atena Parvan-Moldovan
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  3. Fatemeh Koorepazan-Moftakhar
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  4. Ali Reza Ashrafi
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Corresponding author

Correspondence to Mircea V. Diudea .

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Editors and Affiliations

  1. Department of Nanocomputing, Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan, Iran

    Ali Reza Ashrafi

  2. Department of Chemistry, Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, Cluj-Napoca, Romania

    Mircea V. Diudea

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Diudea, M.V., Parvan-Moldovan, A., Koorepazan-Moftakhar, F., Ashrafi, A.R. (2016). Topological Symmetry of Multi-shell Clusters. In: Ashrafi, A., Diudea, M. (eds) Distance, Symmetry, and Topology in Carbon Nanomaterials. Carbon Materials: Chemistry and Physics, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-319-31584-3_5

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