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Properties of Entropy-Based Topological Measures of Fullerenes

Author

Listed:
  • Modjtaba Ghorbani

    (Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Lavizan, Tehran 16785-163, Iran)

  • Matthias Dehmer

    (Department of Computer Science, Swiss Distance University of Applied Sciences, 3900 Brig, Switzerland)

  • Frank Emmert-Streib

    (Predictive Society and Data Analytics Lab, Tampere University, Tampere, Korkeakoulunkatu 10, 33720 Tampere, Finland
    Institute of Biosciences and Medical Technology, Tampere University, Tampere, Korkeakoulunkatu 10, 33720 Tampere, Finland)

Abstract

A fullerene is a cubic three-connected graph whose faces are entirely composed of pentagons and hexagons. Entropy applied to graphs is one of the significant approaches to measuring the complexity of relational structures. Recently, the research on complex networks has received great attention, because many complex systems can be modelled as networks consisting of components as well as relations among these components. Information—theoretic measures have been used to analyze chemical structures possessing bond types and hetero-atoms. In the present article, we reviewed various entropy-based measures on fullerene graphs. In particular, we surveyed results on the topological information content of a graph, namely the orbit-entropy I a ( G ), the symmetry index, a degree-based entropy measure I λ ( G ), the eccentric-entropy If σ ( G ) and the Hosoya entropy H ( G ).

Suggested Citation

  • Modjtaba Ghorbani & Matthias Dehmer & Frank Emmert-Streib, 2020. "Properties of Entropy-Based Topological Measures of Fullerenes," Mathematics, MDPI, vol. 8(5), pages 1-23, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:740-:d:355094
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    References listed on IDEAS

    as
    1. Dehmer, Matthias & Emmert-Streib, Frank & Shi, Yongtang, 2015. "Graph distance measures based on topological indices revisited," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 623-633.
    2. Ghorbani, Modjtaba & Dehmer, Matthias & Rajabi-Parsa, Mina & Emmert-Streib, Frank & Mowshowitz, Abbe, 2019. "Hosoya entropy of fullerene graphs," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 88-98.
    3. Ghorbani, Modjtaba & Dehmer, Matthias & Zangi, Samaneh, 2018. "Graph operations based on using distance-based graph entropies," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 547-555.
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    6. Matthias Dehmer & Abbe Mowshowitz & Frank Emmert-Streib, 2011. "Connections between Classical and Parametric Network Entropies," PLOS ONE, Public Library of Science, vol. 6(1), pages 1-8, January.
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    Cited by:

    1. Maryam Jalali-Rad & Modjtaba Ghorbani & Matthias Dehmer & Frank Emmert-Streib, 2021. "Orbit Entropy and Symmetry Index Revisited," Mathematics, MDPI, vol. 9(10), pages 1-13, May.

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