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Figures of Graph Partitioning by Counting, Sequence and Layer Matrices

Author

Listed:
  • Mihaela Aurelia Tomescu

    (Department of Mathematics-Informatics, University of Petrosani, 332006 Petrosani, Romania)

  • Lorentz Jäntschi

    (Department of Physics and Chemistry, Technical University of Cluj-Napoca, 400641 Cluj-Napoca, Romania
    Chemical Doctoral School, Babes-Bolyai University, 400028 Cluj-Napoca, Romania)

  • Doina Iulia Rotaru

    (Department of Conservative Dentistry, “Iuliu Hatieganu” Medicine and Pharmacy University, 400349 Cluj-Napoca, Romania)

Abstract

A series of counting, sequence and layer matrices are considered precursors of classifiers capable of providing the partitions of the vertices of graphs. Classifiers are given to provide different degrees of distinctiveness for the vertices of the graphs. Any partition can be represented with colors. Following this fundamental idea, it was proposed to color the graphs according to the partitions of the graph vertices. Two alternative cases were identified: when the order of the sets in the partition is relevant (the sets are distinguished by their positions) and when the order of the sets in the partition is not relevant (the sets are not distinguished by their positions). The two isomers of C 28 fullerenes were colored to test the ability of classifiers to generate different partitions and colorings, thereby providing a useful visual tool for scientists working on the functionalization of various highly symmetrical chemical structures.

Suggested Citation

  • Mihaela Aurelia Tomescu & Lorentz Jäntschi & Doina Iulia Rotaru, 2021. "Figures of Graph Partitioning by Counting, Sequence and Layer Matrices," Mathematics, MDPI, vol. 9(12), pages 1-25, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1419-:d:577358
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    References listed on IDEAS

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    1. Hellmann, Tim, 2021. "Pairwise stable networks in homogeneous societies with weak link externalities," European Journal of Operational Research, Elsevier, vol. 291(3), pages 1164-1179.
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    Cited by:

    1. Chuan-Min Lee, 2023. "Clique Transversal Variants on Graphs: A Parameterized-Complexity Perspective," Mathematics, MDPI, vol. 11(15), pages 1-33, July.

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