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On the Wiener Complexity and the Wiener Index of Fullerene Graphs

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  • Andrey A. Dobrynin

    (Laboratory of Topology and Dynamics, Novosibirsk State University, 630090 Novosibirsk, Russia
    Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, 630090 Novosibirsk, Russia)

  • Andrei Yu Vesnin

    (Laboratory of Topology and Dynamics, Novosibirsk State University, 630090 Novosibirsk, Russia
    Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, 630090 Novosibirsk, Russia
    Regional Scientific and Educational Mathematical Center, Tomsk State University, 634050 Tomsk, Russia)

Abstract

Fullerenes are molecules that can be presented in the form of cage-like polyhedra, consisting only of carbon atoms. Fullerene graphs are mathematical models of fullerene molecules. The transmission of a vertex v of a graph is a local graph invariant defined as the sum of distances from v to all the other vertices. The number of different vertex transmissions is called the Wiener complexity of a graph. Some calculation results on the Wiener complexity and the Wiener index of fullerene graphs of order n ≤ 232 and IPR fullerene graphs of order n ≤ 270 are presented. The structure of graphs with the maximal Wiener complexity or the maximal Wiener index is discussed, and formulas for the Wiener index of several families of graphs are obtained.

Suggested Citation

  • Andrey A. Dobrynin & Andrei Yu Vesnin, 2019. "On the Wiener Complexity and the Wiener Index of Fullerene Graphs," Mathematics, MDPI, vol. 7(11), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1071-:d:284703
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    References listed on IDEAS

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    1. Klavžar, Sandi & Azubha Jemilet, D. & Rajasingh, Indra & Manuel, Paul & Parthiban, N., 2018. "General Transmission Lemma and Wiener complexity of triangular grids," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 115-122.
    2. Dobrynin, Andrey A., 2019. "Infinite family of 2-connected transmission irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 1-4.
    3. Andova, Vesna & Orlić, Damir & Škrekovski, Riste, 2017. "Leapfrog fullerenes and Wiener index," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 281-288.
    4. Alizadeh, Yaser & Klavžar, Sandi, 2018. "On graphs whose Wiener complexity equals their order and on Wiener index of asymmetric graphs," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 113-118.
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    Cited by:

    1. Simon Brezovnik & Niko Tratnik & Petra Žigert Pleteršek, 2021. "Weighted Wiener Indices of Molecular Graphs with Application to Alkenes and Alkadienes," Mathematics, MDPI, vol. 9(2), pages 1-16, January.

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